2018年5月27日日曜日

180527(4)

Ruby


Expansion of ((1 + k*x)/(1 - k*x))^(m/k)(4)

s, t を正の数とし、
a(0) = 0, a(1) = 1
n > 1 に対し、
a(n) = s*a(n-1)/(n-1) + t*a(n-2)
で定められる数列{a(n)} を出力してみた。

def A(s, t, n)
  a, b = 0, 1
  ary = [0]
  cnt = 0
  while cnt < n
    a, b = b, s * b / (cnt + 1r) + t * a
    a = a.to_i if a.denominator == 1
    ary << a
    cnt += 1
  end
  ary
end

n = 25
(1..8).each{|i|
  (1..16).each{|j|
    p [i, j, A(i, j, n)]
  }
}

出力結果
[1, 1, [0, 1, 1, (3/2), (3/2), (15/8), (15/8), (35/16), (35/16), (315/128), (315/128), (693/256), (693/256), (3003/1024), (3003/1024), (6435/2048), (6435/2048), (109395/32768), (109395/32768), (230945/65536), (230945/65536), (969969/262144), (969969/262144), (2028117/524288), (2028117/524288), (16900975/4194304)]]
[1, 2, [0, 1, 1, (5/2), (17/6), (137/24), (817/120), (9037/720), (2219/144), (155687/5760), (1753367/51840), (29777027/518400), (415517767/5702400), (1655330579/13685760), (137918196199/889574400), (450088549997/1779148800), (8725180321937/26687232000), (224767684320497/426995712000), (11697095951657/17079828480), (8384064034329317/7685922816000), (208404404807664017/146032533504000), (598208460990722267/265513697280000), (25948570444190817031/8761952010240000), (178909451160543909743/38552588845056000), (1180630458492340277569/192762944225280000), (2322047301948572558731/243490034810880000)]]
[1, 3, [0, 1, 1, (7/2), (25/6), (277/24), (1777/120), (26707/720), (250609/5040), (947477/8064), (8409847/51840), (1337962879/3628800), (1887700859/3628800), (50054364503/43545600), (14361513331/8709120), (2174090875781/609638400), (47412857868431/9144576000), (230394041204393/20901888000), (40301650309070447/2487324672000), (304162751817699973/8954368819200), (42870306976194778487/850665037824000), (1776597992337084624587/17013300756480000), (55793184782342505518207/357279315886080000), (228923454741958345017799/714558631772160000), (579348407358803369129/1200938876928000), (16827201043799488845913283/17149407162531840000)]]
[1, 4, [0, 1, 1, (9/2), (11/2), (155/8), (207/8), (1309/16), (1843/16), (43731/128), (63835/128), (362615/256), (543645/256), (5983055/1024), (9158555/1024), (49172805/2048), (76546627/2048), (3223606147/32768), (5088608019/32768), (26354250067/65536), (42095929945/65536), (430087187061/262144), (694015221361/262144), (3503789789339/524288), (5704460457381/524288), (114022760077975/4194304)]]
[1, 5, [0, 1, 1, (11/2), (41/6), (701/24), (4801/120), (109951/720), (1118161/5040), (31904441/40320), (434442401/362880), (14791440851/3628800), (23066796491/3628800), (910553247551/43545600), (18902654510531/566092800), (847506109781941/7925299200), (20695293345839491/118879488000), (1037702625084168691/1902071808000), (29183301575425876451/32335220736000), (1616868317954203973681/582033973248000), (2711595474312234352889/582033973248000), (164398427269732631720989/11640679464960000), (5858748923325424772787889/244454268764160000), (35056283265127982186206589/488908537528320000), (1382568535629975679927421059/11244896363151360000), (98137910347383206513857606699/269877512715632640000)]]
[1, 6, [0, 1, 1, (13/2), (49/6), (985/24), (1373/24), (36833/144), (382829/1008), (12758717/8064), (178140845/72576), (201938515/20736), (24928161145/1596672), (1144475288305/19160064), (24477234120025/249080832), (1274244248949085/3487131648), (494085526772009/804722688), (373405455545372597/167382319104), (1550846284505759363/406499917824), (696428340372844403633/51218989645824), (1209093914263872204935/51218989645824), (16956098951801040128179/204875958583296), (626339431740792631415419/4302395130249216), (47628645726133275866727607/94652692865482752), (84747615673529552384519117/94652692865482752), (991896085748103039599042075/324523518395940864)]]
[1, 7, [0, 1, 1, (15/2), (19/2), (439/8), (3099/40), (31763/80), (67093/112), (12786561/4480), (20206769/4480), (915266039/44800), (16474478169/492800), (57478686547/394240), (6284103486251/25625600), (372423336790641/358758400), (3203351820526537/1793792000), (211760420423285497/28700672000), (1262188457341162389/97582284800), (51100195870375927391/975822848000), (91042676007059047619/975822848000), (50664825859158663513/136478720000), (91636845852871096294073/136615198720000), (316072896453824628459083/120221374873600), (332479530422215038785083641/69127290552320000), (10288373775953891382644167147/553018324418560000)]]
[1, 8, [0, 1, 1, (17/2), (65/6), (1697/24), (12097/120), (419377/720), (640567/720), (5496139/1152), (396447287/51840), (20182547687/518400), (369056160247/5702400), (21681826517719/68428800), (19290556580239/35582976), (4578714760614977/1779148800), (120322054242048977/26687232000), (685496491894061909/32845824000), (15925426142665963457/426995712000), (259834971793669971421/1537184563200), (4079194616845675079587/13275684864000), (3994362712049085991474657/2920650670080000), (22108770821523605276144311/8761952010240000), (2131132282783441008774763207/192762944225280000), (796760317985313001448755949/38552588845056000), (413161199884347238691998315489/4626310661406720000)]]
[1, 9, [0, 1, 1, (19/2), (73/6), (2125/24), (3053/24), (117803/144), (181691/144), (8663507/1152), (126399275/10368), (1428767989/20736), (2405074949/20736), (156712017761/248832), (271802865089/248832), (2859645300425/497664), (15249283774891/1492992), (1250616053558491/23887872), (2269462513793627/23887872), (204869263190269169/429981696), (378435520034055425/429981696), (7450980578856501169/1719926784), (41935461960657486067/5159780352), (406165265981947198223/10319560704), (772497674682354192607/10319560704), (88504195126782949008775/247669456896)]]
[1, 10, [0, 1, 1, (21/2), (27/2), (867/8), (6267/40), (88789/80), (966169/560), (50688009/4480), (11846503/640), (5151726421/44800), (96369799521/492800), (2298882891747/1971200), (4031629126359/1971200), (325875233970939/27596800), (2930765466441613/137984000), (37661564663313259/315392000), (8235313021364380173/37531648000), (90549558678837154217/75063296000), (3219968506797301619957/1426202624000), (347308291486378487644557/28524052480000), (271983843530098927283607/11745198080000), (539478494229034552736439099/4392704081920000), (3419361244955449182524616177/14433170554880000), (1000618938952986291794272046573/808257551073280000)]]
[1, 11, [0, 1, 1, (23/2), (89/6), (3125/24), (4541/24), (210791/144), (329819/144), (18879427/1152), (280096075/10368), (3794145761/20736), (71577395911/228096), (5580677040883/2737152), (128407488424159/35582976), (1614417560610275/71165952), (8797777748116549/213497856), (861210249750341749/3415965696), (27184161272115056357/58071416832), (2926017861931765383491/1045285502976), (5536464871980453020975/1045285502976), (129852078899393767477799/4181142011904), (749363660087047479836957/12543426035712), (95021972941046922668719031/275955372785664), (4265980104985553195441221693/6346973574070272), (581239399803022467639903177925/152327365777686528)]]
[1, 12, [0, 1, 1, (25/2), (97/6), (3697/24), (26977/120), (1357897/720), (2990861/1008), (927461089/40320), (13847980609/362880), (1015505956729/3628800), (1754076396419/3628800), (29597386833079/8709120), (263970611404751/43545600), (25125775551191111/609638400), (690331716291163631/9144576000), (73052565303721563311/146313216000), (465259057455615930979/497464934400), (270575315082543660132887/44771844096000), (9817691174071782563821967/850665037824000), (1243641127950470872769786687/17013300756480000), (50724804645272254994432500367/357279315886080000), (126281294872776050429638725329/142911726354432000), (1244847766893659348220649296923/714558631772160000), (10769994846099480703935318457099/1008788656619520000)]]
[1, 13, [0, 1, 1, (27/2), (35/2), (1439/8), (10539/40), (190583/80), (2108681/560), (28170621/896), (234953169/4480), (2649408117/6400), (354528888489/492800), (10726406396631/1971200), (50077587003039/5125120), (25629065469444141/358758400), (236396042686975497/1793792000), (26890624130908882137/28700672000), (7250311185479447391/4100096000), (140959071665134101151/11480268800), (25776371437713599583833/1090625536000), (318860494687865990728503/1982955520000), (48082151163827593208580571/152687575040000), (7070027965180012441031673637/3359126650880000), (562355510123196383594912469/134365066035200), (105709886328059228151988332689/3839001886720000)]]
[1, 14, [0, 1, 1, (29/2), (113/6), (4985/24), (7325/24), (426065/144), (4733165/1008), (338768125/8064), (5109798445/72576), (86391527189/145152), (150928131659/145152), (14664704699411/1741824), (26483980326359/1741824), (2900766101410915/24385536), (16152733652181275/73156608), (1965467553800316155/1170505728), (63475077301306611355/19898597376), (8483538077781861019375/358174752768), (312402208196437916187115/6805320302592), (9088964956399187707852423/27221281210368), (376473961795410177143899663/571646905417728), (5378536299980486933775761057/1143293810835456), (247827767696224641014447144029/26295757649215488), (41813156293945427665233528592525/631098183581171712)]]
[1, 15, [0, 1, 1, (31/2), (121/6), (5701/24), (42001/120), (2607451/720), (4152583/720), (317046703/5760), (4801836343/51840), (432814885393/518400), (759622259213/518400), (78666301629953/6220800), (1856182388188373/80870400), (30945026548280009/161740800), (866227101233047859/2426112000), (112268322675041080259/38817792000), (214498523276816255587/38817792000), (30526945645537907925517/698720256000), (1130904370055605299086827/13275684864000), (175134494549621680474533727/265513697280000), (1042833146557133580674506261/796541091840000), (15856907522789327022769354181/1593082183680000), (735411778647211497688178674271/36640890224640000), (132030606067342839246218431292951/879381365391360000)]]
[1, 16, [0, 1, 1, (33/2), (43/2), (2155/8), (3183/8), (70021/16), (111859/16), (9074547/128), (15326235/128), (293450751/256), (517116861/256), (18953220351/1024), (34553419131/1024), (611439253965/2048), (1146472029123/2048), (157674921044163/32768), (302771834811027/32768), (5079238788392219/65536), (9956027071236665/65536), (327062487871349349/262144), (652760136743496529/262144), (10525341442496224307/524288), (21345947916769985637/524288), (1354359020611773373175/4194304)]]
[2, 1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]]
[2, 2, [0, 1, 2, 4, (20/3), (34/3), (268/15), (1288/45), (1976/45), (614/9), (41708/405), (318008/2025), (5223896/22275), (23600476/66825), (90932968/173745), (678564496/868725), (14997074192/13030875), (22231569154/13030875), (32609627108/13030875), (86555574376/23455575), (12018048214696/2228279625), (6787447674196/857030625), (385751966373608/33424194375), (6209382070833776/367666138125), (361059581089936/14706645525), (39512914806814756/1102998414375)]]
[2, 3, [0, 1, 2, 5, (28/3), (59/3), (538/15), (3193/45), (8056/63), (77123/315), (1241806/2835), (1664773/2025), (20745892/14175), (23050729/8505), (204444358/42525), (2624770903/297675), (69649514576/4465125), (126820879957/4465125), (108736200094/2168775), (62016550903553/683164125), (2076391574494876/12980118375), (18712912794760043/64900591875), (691489171555406026/1362912429375), (49671046321178603/54516497175), (2182448050147041128/1362912429375), (1674513919257420851/584105326875)]]
[2, 4, [0, 1, 2, 6, 12, 30, 60, 140, 280, 630, 1260, 2772, 5544, 12012, 24024, 51480, 102960, 218790, 437580, 923780, 1847560, 3879876, 7759752, 16224936, 32449872, 67603900]]
[2, 5, [0, 1, 2, 7, (44/3), (127/3), (1354/15), (10879/45), (163928/315), (421747/315), (1174322/405), (103113329/14175), (224254228/14175), (1658827049/42525), (47047228558/552825), (801813535853/3869775), (26303422064656/58046625), (1294366182593/1184625), (2362638761389874/986792625), (50881955115888479/8881133625), (111674739537901012/8881133625), (1327886247666162481/44405668125), (61285010752730356262/932519030625), (144999420618831638347/932519030625), (1048253582543093463832/3063991100625), (51859243882947328791421/64343813113125)]]
[2, 6, [0, 1, 2, 8, (52/3), (170/3), (380/3), (3440/9), (54760/63), (158170/63), (3273380/567), (9195856/567), (234434792/6237), (1937996884/18711), (58733735096/243243), (1116880033760/1702701), (7847202635600/5108103), (1621903149010/392931), (842584150705460/86837751), (20198376330990800/781539759), (47625689015041240/781539759), (11450256989768084/71049069), (367808380568829064/965431467), (180823360535674302752/180535684329), (428404773479589192656/180535684329), (3361921683012034747700/541607052987)]]
[2, 7, [0, 1, 2, 9, 20, 73, (846/5), (2837/5), (47128/35), (30159/7), (363406/35), (5641231/175), (151193772/1925), (459573749/1925), (587111230/1001), (307426258863/175175), (3801007122992/875875), (11235044950579/875875), (474789937537206/14889875), (277944957324607/2977975), (3469816382404972/14889875), (50375275723008711/74449375), (883688530837890614/521145625), (28035962145539585843/5732601875), (324216862480996689816/26369968625), (4648880264798955274813/131849843125)]]
[2, 8, [0, 1, 2, 10, (68/3), (274/3), (3268/15), (36148/45), (17752/9), (311374/45), (7013468/405), (119108108/2025), (3324142136/22275), (6621322316/13365), (1103345569592/868725), (3600708399976/868725), (139602885150992/13030875), (449535368640994/13030875), (46788383806628/521235), (33536256137317268/117277875), (1667235238461312136/2228279625), (2392833843962889068/1012854375), (207588563553526536248/33424194375), (1431275609284351277944/73533227625), (18890087335877444441104/367666138125), (9288189207794290234924/58052548125)]]
[2, 9, [0, 1, 2, 11, (76/3), (335/3), (818/3), (9863/9), (24904/9), (94993/9), (2207210/81), (8135875/81), (21344140/81), (230340695/243), (611728810/243), (2160456085/243), (17380860304/729), (60504921833/729), (163545968834/729), (5064444637307/6561), (13780322911060/6561), (46958034026869/6561), (385485299749154/19683), (1302911036884477/19683), (3582664309645384/19683), (36074264073292225/59049)]]
[2, 10, [0, 1, 2, 12, 28, 134, (1668/5), (7256/5), (131272/35), (540738/35), (1432884/35), (4067112/25), (845025768/1925), (3272513868/1925), (8953721352/1925), (238029692112/13475), (3292488934608/67375), (12313045722426/67375), (83478458618316/163625), (2158145462848888/1145375), (10485694626187096/1978375), (2107909510150472628/108810625), (41775197317587301352/761674375), (1664865520133451224912/8378418125), (109020980253762774870384/192703616875), (56000593045501049471756/27529088125)]]
[2, 11, [0, 1, 2, 13, (92/3), (475/3), (1202/3), (16877/9), (44488/9), (196769/9), (4797850/81), (20439701/81), (621419252/891), (7730321089/2673), (282049501286/34749), (1145728701625/34749), (751225001776/8019), (39029787781511/104247), (1904287554880478/1772199), (67591420391163491/15949791), (195639354290131900/15949791), (763069559731811591/15949791), (6674118565783441726/47849373), (283668368748431049259/526343103), (19141408706072180421976/12105891369), (220089644056577211493075/36317674107)]]
[2, 12, [0, 1, 2, 14, (100/3), (554/3), (7108/15), (106828/45), (2004872/315), (1894954/63), (33639388/405), (5351851516/14175), (15101606872/14175), (200217458012/42525), (114892106648/8505), (17392727006248/297675), (758605725894896/4465125), (460788082408786/637875), (161206601236281788/75907125), (1216651007270799892/136632825), (342962455809558227896/12980118375), (7106391969348338498348/64900591875), (446345478258740044145656/1362912429375), (1831387637935666760142392/1362912429375), (9269574517740853906064/2290609125), (67308804175197955383653132/4088737288125)]]
[2, 13, [0, 1, 2, 15, 36, 213, (2766/5), (14767/5), (56248/7), (1414107/35), (3970366/35), (95887321/175), (3030586332/1925), (568679385/77), (540603059358/25025), (17359295870733/175175), (257547255921712/875875), (1160547638587859/875875), (696929868657342/175175), (15474302562007357/875875), (891656992915832084/16641625), (19556592160537001937/83208125), (418741659883728266178/582456875), (3998978082516253441023/1281405125), (61618743486206295733464/6407025625), (265068470654073664977617/6407025625)]]
[2, 14, [0, 1, 2, 16, (116/3), (730/3), (1916/3), (32576/9), (628456/63), (3349562/63), (85884580/567), (439221728/567), (1282242616/567), (19088433884/1701), (56790872008/1701), (1927457392640/11907), (17467499327408/35721), (83136647906806/35721), (4323538135736716/607257), (182402237952115168/5465313), (10715354772857928440/103840947), (49590530772548427532/103840947), (3249495364765327816424/2180659887), (14875024716653358404992/2180659887), (1076087556887742273698512/50155177401), (861076221500534105155700/8850913659)]]
[2, 15, [0, 1, 2, 17, (124/3), (827/3), (10954/15), (197029/45), (549224/45), (3092741/45), (80330722/405), (2167930897/2025), (6418973404/2025), (100766377067/6075), (3956632195474/78975), (20214676698847/78975), (930671597379344/1184625), (4664636206912993/1184625), (14508854690915218/1184625), (644234742624169273/10661625), (38503681767445872716/202570875), (72098949932551088491/77911875), (8931124497424796832638/3038563125), (42989806119399186479293/3038563125), (3167217563850353280218696/69886951875), (45286253724540746326122929/209660855625)]]
[2, 16, [0, 1, 2, 18, 44, 310, 828, 5236, 14744, 87462, 255340, 1450460, 4349160, 23932220, 73268440, 393382440, 1224746032, 6447212294, 20354432076, 105417000268, 336767439560, 1720348748244, 5552121770888, 28030318314712, 91271367318096, 456091040311900]]
[3, 1, [0, 1, 3, (11/2), (17/2), (95/8), (125/8), (315/16), (385/16), (3675/128), (4305/128), (9933/256), (11319/256), (51051/1024), (57057/1024), (126555/2048), (139425/2048), (2443155/32768), (2661945/32768), (5773625/65536), (6235515/65536), (26835809/262144), (28775747/262144), (61519549/524288), (65575783/524288), (557732175/4194304)]]
[3, 2, [0, 1, 3, (13/2), (25/2), (179/8), (1537/40), (5117/80), (8341/80), (21379/128), (507263/1920), (2645163/6400), (135404327/211200), (833727359/844800), (3316646417/2196480), (50460922133/21964800), (29394274141/8448000), (9220124232779/1757184000), (13855098789617/1757184000), (24899317916593/2108620800), (1177484097593857/66772992000), (105214764961398113/4006379520000), (156328772420033999/4006379520000), (5098435975561618969/88140349440000), (1508695874919645773/17628069888000), (89118454983584132369/705122795520000)]]
[3, 3, [0, 1, 3, (15/2), (33/2), (279/8), (2817/40), (11187/80), (30375/112), (2335041/4480), (4423347/4480), (83321271/44800), (155424393/44800), (231055929/35840), (2131695711/179200), (54916832223/2508800), (502572931533/12544000), (14687758528119/200704000), (90832557543057/682393600), (1649538965773233/6823936000), (56723174696862189/129654784000), (2050643945072072187/2593095680000), (25874377317754191567/18151669760000), (18636738810482907729/7260667904000), (167400658782927045747/36303339520000), (2403809316040875973227/290426716160000)]]
[3, 4, [0, 1, 3, (17/2), (41/2), (395/8), (893/8), (4053/16), (8881/16), (156339/128), (336305/128), (1452495/256), (3086575/256), (26326495/1024), (55460545/1024), (234380765/2048), (490560513/2048), (16472050499/32768), (34302705273/32768), (143210639083/65536), (297033848355/65536), (2469590534341/262144), (5105340221443/262144), (21149089789667/524288), (43601298700631/524288), (720372171969975/4194304)]]
[3, 5, [0, 1, 3, (19/2), (49/2), (527/8), (6481/40), (32831/80), (552163/560), (10849169/4480), (77108729/13440), (88509597/6400), (4362355051/134400), (41536385791/537600), (1258821470633/6988800), (41574575481709/97843200), (482162090203259/489216000), (18076316463293377/7827456000), (101424198866616053/19009536000), (9928890788345934641/798400512000), (7622267120049751849/266133504000), (1061489482915041230741/15968010240000), (1004014731471736477273/6575063040000), (78959241195421846182863/223552143360000), (4162575323640755164686019/5141699297280000), (10972153889061264807559997/5876227768320000)]]
[3, 6, [0, 1, 3, (21/2), (57/2), (675/8), (1773/8), (9873/16), (178551/112), (3852981/896), (1407825/128), (52148637/1792), (1457276211/19712), (15224516379/78848), (500343726969/1025024), (18126203066775/14350336), (45654113678751/14350336), (268153976492379/32800768), (80138747030061591/3903291392), (409636794107804409/7806582784), (93304041651566775/709689344), (10447089733487646531/31226331136), (182872958705583046731/218584317952), (10201729789859334534837/4808854994944), (3638555850929988406707/686979284992), (30303112992338704501125/2262990585856)]]
[3, 7, [0, 1, 3, (23/2), (65/2), (839/8), (11617/40), (70347/80), (1349507/560), (6324909/896), (86113907/4480), (2472059871/44800), (73723888003/492800), (835118328271/1971200), (5868170043581/5125120), (1151963300870969/358758400), (15528979907644419/1793792000), (53206645246975069/2207744000), (31642236908787001467/487911424000), (7006750907882794559/39032913920), (470649543990976420113/975822848000), (2357779709960246383349/1774223360000), (487172129920719601927579/136615198720000), (29420068190470760419535179/3005534371840000), (362764777750120222257218071/13825458110464000), (39706871718076940531647400907/553018324418560000)]]
[3, 8, [0, 1, 3, (25/2), (73/2), (1019/8), (14737/40), (96257/80), (55409/16), (6991583/640), (60184223/1920), (619510863/6400), (58537714007/211200), (142548237067/168960), (26489912582917/10982400), (159602986228073/21964800), (2278795992861433/109824000), (108982299164551019/1757184000), (62183611505413309/351436800), (5542068417425515457/10543104000), (100061157905653745137/66772992000), (1613494400920404608683/364216320000), (50564846996160147765119/4006379520000), (655083940234076753141129/17628069888000), (9326641727998583889144289/88140349440000), (218953502602903144894305569/705122795520000)]]
[3, 9, [0, 1, 3, (27/2), (81/2), (1215/8), (3645/8), (25515/16), (76545/16), (2066715/128), (6200145/128), (40920957/256), (122762871/256), (1595917323/1024), (4787751969/1024), (30778405515/2048), (92335216545/2048), (4709096043795/32768), (14127288131385/32768), (89472824832105/65536), (268418474496315/65536), (3382072778653569/262144), (10146218335960707/262144), (63644460471026253/524288), (190933381413078759/524288), (4773334535326968975/4194304)]]
[3, 10, [0, 1, 3, (29/2), (89/2), (1427/8), (22081/40), (164781/80), (3585683/560), (103034409/4480), (321199443/4480), (11267039229/44800), (387120504987/492800), (5344617765747/1971200), (16718193530037/1971200), (798401067794691/27596800), (12501136538820591/137984000), (676224263852214573/2207744000), (36031764177148651239/37531648000), (241926837768802505233/75063296000), (14417850900622894986519/1426202624000), (962575536223318204844957/28524052480000), (21147566797095371185971557/199668367360000), (1545809026175196149019148451/4392704081920000), (6567300886578127449886677869/5943070228480000), (2955932723234189080843306673613/808257551073280000)]]
[3, 11, [0, 1, 3, (31/2), (97/2), (1655/8), (5261/8), (41671/16), (133601/16), (4067851/128), (39338515/384), (97360425/256), (10396164455/8448), (151763501555/33792), (6401896572925/439296), (46148031404555/878592), (150071330885261/878592), (8572267519857463/14057472), (474730224568273301/238977024), (10092814381848346787/1433862144), (10975265697441399295/477954048), (35679947004363213643/441188352), (1514997830784653532277/5735448576), (116794106768080630717709/126179868672), (8782860246451623452806909/2902136979456), (245174132345046820025449925/23217095835648)]]
[3, 12, [0, 1, 3, (33/2), (105/2), (1899/8), (30897/40), (258777/80), (5967027/560), (38359845/896), (636767667/4480), (3560887143/6400), (83210177313/44800), (1279668257361/179200), (857879314083/35840), (227852456947893/2508800), (3830945576096493/12544000), (230231195398266759/200704000), (1884985706653393347/487424000), (19666525540936817763/1364787200), (6311872258751683830069/129654784000), (467332399109614496486607/2593095680000), (11071277793812443331002527/18151669760000), (81531282448727719954568847/36303339520000), (55269036430701320683279143/7260667904000), (1157621185318766817007857861/41489530880000)]]
[3, 13, [0, 1, 3, (35/2), (113/2), (2159/8), (35857/40), (316527/80), (1495111/112), (252858321/4480), (123106261/640), (35456813211/44800), (1338664112243/492800), (4323992253787/394240), (969796823683073/25625600), (54062218833349429/358758400), (936577328384945859/1793792000), (8433491367405463391/4100096000), (41045185316290391631/5740134400), (1603304071061611656547/57401344000), (106191519944422102298211/1090625536000), (8238896670877627890236813/21812510720000), (201507462969725854072980833/152687575040000), (136790348192049508787784337/26873013207040), (1221661465826863561568311487/68553605120000), (1838135938322159928758043643863/26873013207040000)]]
[3, 14, [0, 1, 3, (37/2), (121/2), (2435/8), (8237/8), (76417/16), (1843703/112), (65442037/896), (684926245/2688), (1969362285/1792), (20789231275/5376), (351642095155/21504), (1245345127205/21504), (72657886031995/301056), (258619222138579/301056), (17051224137582617/4816896), (1035975670316456683/81887232), (25385123738784433759/491323392), (576524180347139389115/3111714816), (28047515182691488419983/37340577792), (706039951270927410019223/261384044544), (5689869326154148296685547/522768089088), (471759336596939696942436253/12023666049024), (15128862720770025709204405325/96189328392192)]]
[3, 15, [0, 1, 3, (39/2), (129/2), (2727/8), (46881/40), (455931/80), (1601829/80), (59517207/640), (212058549/640), (9563756697/6400), (34417079631/6400), (608242481451/25600), (28670049556533/332800), (249501731861547/665600), (350000705026269/256000), (313052105729880891/53248000), (1147246688928408849/53248000), (9773978734872563013/106496000), (683252548893810732969/2023424000), (57761436435455041373007/40468480000), (213227398444636797229701/40468480000), (1790996019912188549525583/80936960000), (152499892986535955737070439/1861550080000), (5095648907944176352427679519/14892400640000)]]
[3, 16, [0, 1, 3, (41/2), (137/2), (3035/8), (10589/8), (107709/16), (385009/16), (14941779/128), (54261745/128), (510693975/256), (1875656015/256), (34560070415/1024), (128017385825/1024), (1160786847205/2048), (4328713715841/2048), (310147574032003/32768), (1162882636084473/32768), (10312349914385587/65536), (38840510130658755/65536), (683294700599072821/262144), (2583406177019170723/262144), (22569995740175558651/524288), (85612910152462449047/524288), (2974572364894933956375/4194304)]]
[4, 1, [0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625]]
[4, 2, [0, 1, 4, 10, (64/3), (124/3), (1136/15), (5992/45), (2048/9), (17104/45), (252736/405), (2044832/2025), (35980288/22275), (6837568/2673), (3490219264/868725), (5441624704/868725), (126473076736/13030875), (194867010304/13030875), (59759442944/2606175), (4105200614912/117277875), (118609449893888/2228279625), (81690687884288/1012854375), (4071767820660736/33424194375), (13490195009062912/73533227625), (101309496410243072/367666138125), (455360598477008896/1102998414375)]]
[4, 3, [0, 1, 4, 11, (80/3), (179/3), (1916/15), (11887/45), (168256/315), (66751/63), (5877932/2835), (56812789/14175), (108828176/14175), (620143277/42525), (46810676/1701), (15363542617/297675), (430088243968/4465125), (798881478757/4465125), (25130026357396/75907125), (83389330292851/136632825), (14559490127201168/12980118375), (133389285794513843/64900591875), (5119796533246423292/1362912429375), (9334397102008267253/1362912429375), (3396552601756837184/272582485875), (92500955422466498237/4088737288125)]]
[4, 4, [0, 1, 4, 12, 32, 80, 192, 448, 1024, 2304, 5120, 11264, 24576, 53248, 114688, 245760, 524288, 1114112, 2359296, 4980736, 10485760, 22020096, 46137344, 96468992, 201326592, 419430400]]
[4, 5, [0, 1, 4, 13, (112/3), (307/3), (4028/15), (31081/45), (547264/315), (1361467/315), (30072748/2835), (52353653/2025), (885082544/14175), (6382216109/42525), (198119960516/552825), (3300148250627/3869775), (9016428636416/4465125), (276814511865377/58046625), (1581487384385884/140970375), (233903924958415781/8881133625), (547411457651746256/8881133625), (6395009581612140781/44405668125), (312971053593615347524/932519030625), (728379833995386663373/932519030625), (38905190499247311618752/21447937704375), (2275156621664134913219/540704311875)]]
[4, 6, [0, 1, 4, 14, (128/3), (380/3), (1072/3), (8984/9), (171008/63), (462832/63), (1583680/81), (29427232/567), (849369088/6237), (6675961024/18711), (225456210688/243243), (4095987140480/1702701), (31684272259072/5108103), (11664119513344/729729), (3558391116798976/86837751), (82070414226346496/781539759), (209431102249533440/781539759), (534308705807985664/781539759), (28525553706673156096/16412334939), (797602973663214442496/180535684329), (288771443611072724992/25790812047), (15367553578576614502400/541607052987)]]
[4, 7, [0, 1, 4, 15, 48, 153, (2292/5), (6883/5), (27968/7), (407187/35), (1159852/35), (16571249/175), (512828016/1925), (289385769/385), (52455064836/25025), (1026603803937/175175), (14220295956736/875875), (39486207126979/875875), (14801280378876/119119), (5110005325301501/14889875), (1275173720574256/1353625), (192877097311869351/74449375), (217280155295888964/30655625), (22269656146231560993/1146520375), (6987046758417960259008/131849843125), (19091580990786066642533/131849843125)]]
[4, 8, [0, 1, 4, 16, (160/3), (544/3), (8576/15), (82432/45), (252928/45), (157184/9), (21354496/405), (325640192/2025), (10698539008/22275), (96667549696/66825), (744922873856/173745), (11117600702464/868725), (491424127123456/13030875), (1456968116076544/13030875), (4274209044299776/13030875), (22690024489222144/23455575), (6300918462386536448/2228279625), (7117154732417744896/857030625), (808980507784344764416/33424194375), (26044036057226390011904/367666138125), (3028787290407685849088/14706645525), (662916706503529433399296/1102998414375)]]
[4, 9, [0, 1, 4, 17, (176/3), (635/3), (2092/3), (21329/9), (68672/9), (226297/9), (6467620/81), (20917105/81), (65814800/81), (630576635/243), (1971023180/243), (6238339195/243), (58208297216/729), (182987232569/729), (566930494372/729), (15955826826833/6561), (49280491481360/6561), (153458539737769/6561), (1418263864132588/19683), (4401246730034779/19683), (13529808991112384/19683), (125598566206495225/59049)]]
[4, 10, [0, 1, 4, 18, 64, 244, (4176/5), (14984/5), (352256/35), (1225008/35), (4067008/35), (69384416/175), (2514392064/1925), (8470416448/1925), (27750202624/1925), (648429556608/13475), (10577143660544/67375), (35065763745536/67375), (1938377477274624/1145375), (6391930387246592/1145375), (393859442231164928/21762125), (587835755465038848/9891875), (146472395861061627904/761674375), (5271913640511002298368/8378418125), (391662816090529927790592/192703616875), (1277817273332618849923072/192703616875)]]
[4, 11, [0, 1, 4, 19, (208/3), (835/3), (2956/3), (33467/9), (116672/9), (426473/9), (13256420/81), (47523395/81), (1794120400/891), (19045112785/2673), (845858102740/34749), (2965124871895/34749), (30285417287936/104247), (8109267314963/8019), (6085054933222108/1772199), (189592769450519693/15949791), (642334705641729680/15949791), (2213987405084062559/15949791), (22462180946225115188/47849373), (848601789937964939293/526343103), (65906656733096355325376/12105891369), (677042086929463566586075/36317674107)]]
[4, 12, [0, 1, 4, 20, (224/3), (944/3), (17216/15), (204352/45), (1031168/63), (19743488/315), (635804672/2835), (1704727552/2025), (42487586816/14175), (94415785984/8505), (1674808180736/42525), (43004246474752/297675), (2282275293626368/4465125), (8311333188861952/4465125), (14252271218720768/2168775), (16257266720060997632/683164125), (1088627185808769548288/12980118375), (19621911246678306848768/64900591875), (1450157899105762858237952/1362912429375), (208335468269104699277312/54516497175), (18307701173047870382669824/1362912429375), (28093681718388309220130816/584105326875)]]
[4, 13, [0, 1, 4, 21, 80, 353, (6612/5), (27353/5), (711104/35), (568935/7), (1501236/5), (205921179/175), (8337370896/1925), (32225852229/1925), (307583818068/5005), (41199021367587/175175), (754685214594816/875875), (409515384648837/125125), (10485403717389516/875875), (7919197943603923/175175), (2748278677067288912/16641625), (4695393270801955767/7564375), (1319332566037378472876/582456875), (54339640436875091896189/6407025625), (5660426548378184055744/183057875), (38917604239206084296963/337211875)]]
[4, 14, [0, 1, 4, 22, (256/3), (1180/3), (4528/3), (58616/9), (1565696/63), (6527216/63), (223386560/567), (911783840/567), (3458969600/567), (41753890880/1701), (158124074240/1701), (4408129454720/11907), (50014981390336/35721), (197645182445824/35721), (12694146300683264/607257), (448744273400321536/5465313), (32184763337437020160/103840947), (125802929391972932608/103840947), (9965532138774375657472/2180659887), (38797976175562655942656/2180659887), (197887838434564681498624/2950304553), (39160891612287325433344000/150465532203)]]
[4, 15, [0, 1, 4, 23, (272/3), (1307/3), (25628/15), (345331/45), (1350592/45), (5855261/45), (205750964/405), (4363803103/2025), (17018159792/2025), (213389299427/6075), (10809180676028/78975), (44699250724273/78975), (2610862655003392/1184625), (10710047076712273/1184625), (41682950901924356/1184625), (1529222257160005567/10661625), (113033658092075995408/202570875), (2292175374545083928383/1012854375), (26742387570457146925876/3038563125), (108010144140066439854667/3038563125), (9658164288367981448845888/69886951875), (116619581329152755974003289/209660855625)]]
[4, 16, [0, 1, 4, 24, 96, 480, 1920, 8960, 35840, 161280, 645120, 2838528, 11354112, 49201152, 196804608, 843448320, 3373793280, 14338621440, 57354485760, 242163384320, 968653537280, 4068344856576, 16273379426304, 68052313964544, 272209255858176, 1134205232742400]]
[5, 1, [0, 1, 5, (27/2), (55/2), (383/8), (603/8), (1771/16), (2471/16), (26523/128), (34503/128), (87549/256), (108801/256), (531531/1024), (639639/1024), (1519947/2048), (1785927/2048), (33248787/32768), (38353887/32768), (87805289/65536), (99814429/65536), (451035585/262144), (506647141/262144), (1132365325/524288), (1259460657/524288), (11158023695/4194304)]]
[5, 2, [0, 1, 5, (29/2), (205/6), (1721/24), (3361/24), (37457/144), (67087/144), (934747/1152), (14334263/10368), (47985155/20736), (870633347/228096), (17021247655/2737152), (356743842539/35582976), (1139921908445/71165952), (5420848018913/213497856), (136536743305285/3415965696), (213625002283241/3415965696), (5983447770406465/61487382528), (16003340037615379/106205478912), (1085520801515551849/4673041072128), (5000253771012997091/14019123216384), (168290014655117829523/308420710760448), (256595951719162704509/308420710760448), (9360900462041469339649/7402097058250752)]]
[5, 3, [0, 1, 5, (31/2), (245/6), (2341/24), (5281/24), (68543/144), (1008121/1008), (16555829/8064), (300533281/72576), (170649721/20736), (2346176071/145152), (54734610047/1741824), (105514111651/1741824), (2826424180229/24385536), (16121202248255/73156608), (487611093194251/1170505728), (2227565214363905/2842656768), (525591766055059093/358174752768), (18626332199836861175/6805320302592), (138461254860390334379/27221281210368), (5386141988660840687995/571646905417728), (19894364470891382444479/1143293810835456), (36641713773463170746335/1143293810835456), (230800401538785055676309/3919864494292992)]]
[5, 4, [0, 1, 5, (33/2), (95/2), (1003/8), (2523/8), (12229/16), (28919/16), (535923/128), (1223143/128), (5510527/256), (12289929/256), (108651647/1024), (238427959/1024), (1039518861/2048), (2253929959/2048), (77798856899/32768), (167133534111/32768), (715242818587/65536), (1525290067253/65536), (12969175164645/262144), (27492539924773/262144), (116250010373875/524288), (245212060783809/524288), (4128687099937015/4194304)]]
[5, 5, [0, 1, 5, (35/2), (325/6), (3725/24), (10225/24), (162875/144), (2961625/1008), (60413125/8064), (195464375/10368), (6805431875/145152), (16775884375/145152), (492205334375/1741824), (15546216484375/22643712), (525637936703125/317011968), (3790343398421875/951035904), (1594558481328125/167215104), (5880391130858046875/258681765888), (251412333009605078125/4656271785984), (595396342042909765625/4656271785984), (5623643002235011328125/18625087143936), (278184678669197158203125/391126830022656), (1307412611682623814453125/782253660045312), (10074219878904066494140625/2570262025863168), (3961056504005684055185546875/431804020345012224)]]
[5, 6, [0, 1, 5, (37/2), (365/6), (4489/24), (13249/24), (227849/144), (4477993/1008), (98947229/8064), (2429229121/72576), (13115529853/145152), (386235893237/1596672), (12318679109761/19160064), (423110191618637/249080832), (15567548545952197/3487131648), (122191316833848721/10461394944), (5094410565403476341/167382319104), (224888281899858494377/2845499424768), (10477779207580075033961/51218989645824), (27045244762968947664811/51218989645824), (1947635984230005234125/1432699011072), (15023363089260803365464119/4302395130249216), (847151929051141171613534095/94652692865482752), (2167247390619630646765945033/94652692865482752), (132826114736462481946178634845/2271664628771586048)]]
[5, 7, [0, 1, 5, (39/2), (135/2), (1767/8), (5547/8), (33983/16), (713521/112), (16888941/896), (49339921/896), (285785095/1792), (9027273309/19712), (103067264775/78848), (3801263808351/1025024), (150314014365105/14350336), (32509886513341/1103872), (18948312232258925/229605376), (899426272139511057/3903291392), (5009379573577352515/7806582784), (13910225592473510723/7806582784), (154172853652639381143/31226331136), (2983358972212540403613/218584317952), (181115131098607954890219/4808854994944), (674860772651168110826373/6506097934336), (252397344080123475705349307/884829319069696)]]
[5, 8, [0, 1, 5, (41/2), (445/6), (6161/24), (20401/24), (397733/144), (1263343/144), (31771627/1152), (886543703/10368), (5461657991/20736), (183339981683/228096), (6684210746911/2737152), (262229350874939/35582976), (1577622514553873/71165952), (14164631356550945/213497856), (676630202371441957/3415965696), (2012081696688945065/3415965696), (107495157624932367133/61487382528), (6042531310265615533505/1168260268032), (71399587146224494750369/4673041072128), (631082710889945158895315/14019123216384), (40854395567656259022671407/308420710760448), (119951947457425186883547485/308420710760448), (8443803686277127666770647569/7402097058250752)]]
[5, 9, [0, 1, 5, (43/2), (485/6), (7069/24), (24529/24), (504371/144), (1684831/144), (44738867/1152), (1315464823/10368), (8563161277/20736), (27570712849/20736), (1062674982161/248832), (3386358134677/248832), (21546976917953/497664), (204410316190511/1492992), (10330345609508251/23887872), (32473422475406599/23887872), (1835883101117369657/429981696), (5743821572888861053/429981696), (71835613213114168705/1719926784), (671643882167078542799/5159780352), (4184415787220473538615/10319560704), (12999245484924908017907/10319560704), (968830037464246824430375/247669456896)]]
[5, 10, [0, 1, 5, (45/2), (175/2), (2675/8), (9675/8), (69625/16), (1702625/112), (47503125/896), (162600625/896), (158951875/256), (41335453125/19712), (558464196875/78848), (1868212046875/78848), (87526047796875/1103872), (290725035828125/1103872), (15457792826640625/17661952), (124008723083671875/42893312), (5737905706383203125/600506368), (358552731934483203125/11409620992), (429032824435065234375/4148953088), (108260366722964826171875/319469387776), (7809117879544829201171875/7028326531072), (586843045015926166435546875/161651510214656), (313200992654197877705078125/26392083300352)]]
[5, 11, [0, 1, 5, (47/2), (565/6), (9029/24), (33889/24), (765359/144), (2783359/144), (81268387/1152), (2610762263/10368), (18701902889/20736), (725313982091/228096), (30781732905283/2737152), (1398547457794571/35582976), (9802538080764203/71165952), (102106670295205889/213497856), (5686273458119528629/3415965696), (333934524813853663033/58071416832), (20809669084099601680379/1045285502976), (71595264619485025722739/1045285502976), (987220704319867499659415/4181142011904), (10155732575714785895158273/12543426035712), (767500894214797734228526655/275955372785664), (60364311987502486963593580793/6346973574070272), (291887469977044957473740103125/8960433281040384)]]
[5, 12, [0, 1, 5, (49/2), (605/6), (10081/24), (39121/24), (921437/144), (24324169/1008), (740826509/8064), (3531459223/10368), (184738740505/145152), (677257304239/145152), (29988665153915/1741824), (109059153792691/1741824), (5583391514821175/24385536), (60549205026337439/73156608), (502682791095526285/167215104), (215226502894308820871/19898597376), (13997090976790951733995/358174752768), (953275022762198159524559/6805320302592), (13718621993595546140927999/27221281210368), (60558490171310204441493851/33626288553984), (7382137454277734107530163981/1143293810835456), (3758953782850705770289621849/163327687262208), (118822051012198006575201262697/1444160603160576)]]
[5, 13, [0, 1, 5, (51/2), (215/2), (3727/8), (14907/8), (121747/16), (3321809/112), (105240861/896), (403935281/896), (3140197667/1792), (131226478701/19712), (2014903863359/78848), (98783618918671/1025024), (5261180635300749/14350336), (19732345521631705/14350336), (1192987299750714317/229605376), (4455206486073134145/229605376), (33492784508003646767/459210752), (215303266060013318315/793182208), (35459207020567749507261/34900017152), (921172955671906242378695/244300120064), (75595197233536165725429997/5374602641408), (279889203851194786564965465/5374602641408), (8328382518706419213052995463/42996821131264)]]
[5, 14, [0, 1, 5, (53/2), (685/6), (12329/24), (50689/24), (1289081/144), (36250537/1008), (1191892189/8064), (42500002241/72576), (342856833869/145152), (1345844078143/145152), (64329168480707/1741824), (250843793005219/1741824), (13862735987244667/24385536), (161358886274313439/73156608), (10122553014799983419/1170505728), (665067404006585492807/19898597376), (46690354135436056431031/358174752768), (3417794501060711621715071/6805320302592), (53096331301164675664332055/27221281210368), (4284807989753220245458583771/571646905417728), (33168282800427202129472059145/1143293810835456), (2925257759403209848722688244249/26295757649215488), (270950778278717467300173514293805/631098183581171712)]]
[5, 15, [0, 1, 5, (55/2), (725/6), (13525/24), (57025/24), (1502375/144), (6205375/144), (211311875/1152), (7758364375/10368), (64812570625/20736), (262211190625/20736), (12977318665625/248832), (678460779390625/3234816), (5545769122015625/6469632), (66607239267171875/19408896), (4325989964187109375/310542336), (17258087413588046875/310542336), (1254307727398459765625/5589762048), (94805527068698979296875/106205478912), (1524716336302943112109375/424821915648), (18154077969725061353515625/1274465746944), (145476323889867180705078125/2548931493888), (13253695418559628237451171875/58625424359424), (1270812438900898397425302734375/1407010184626176)]]
[5, 16, [0, 1, 5, (57/2), (255/2), (4923/8), (21243/8), (192941/16), (817591/16), (28784403/128), (120642983/128), (1041743879/256), (4334095401/256), (73895100591/1024), (305803298199/1024), (2583074146197/2048), (10646730257767/2048), (714500632715267/32768), (2935710190904607/32768), (24494970352946659/65536), (100388770938670229/65536), (1668066873527256405/262144), (6822040119486146181/262144), (56479067279911362315/524288), (230583341927885234817/524288), (7613626181708463101015/4194304)]]
[6, 1, [0, 1, 6, 19, 44, 85, 146, 231, 344, 489, 670, 891, 1156, 1469, 1834, 2255, 2736, 3281, 3894, 4579, 5340, 6181, 7106, 8119, 9224, 10425]]
[6, 2, [0, 1, 6, 20, 52, 118, (1228/5), (2408/5), 904, (8206/5), (43532/15), (125592/25), (7049176/825), (2362732/165), (254160536/10725), (416081104/10725), (3373767568/53625), (417382606/4125), (1732516948/10725), (41218428008/160875), (37419552376/92625), (9683769164132/15283125), (15115243473832/15283125), (10335546081296/6724575), (399941091737104/168114375), (616762576999076/168114375)]]
[6, 3, [0, 1, 6, 21, 60, 153, (1818/5), (4113/5), (62856/35), (26703/7), (39654/5), (2835459/175), (5710284/175), (11361519/175), (4474926/35), (305715789/1225), (2960767728/6125), (813717819/875), (185175302526/104125), (14088894489/4165), (12668326417332/1978375), (119385862860123/9891875), (92290941149418/4073125), (2934997483573521/69243125), (22336691902344/282625), (10173114829739133/69243125)]]
[6, 4, [0, 1, 6, 22, 68, 190, 500, 1260, 3080, 7350, 17220, 39732, 90552, 204204, 456456, 1012440, 2230800, 4886310, 10647780, 23094500, 49884120, 107343236, 230205976, 492156392, 1049212528, 2230928700]]
[6, 5, [0, 1, 6, 23, 76, 229, (3274/5), (8999/5), (168584/35), (441403/35), (3411566/105), (14446641/175), (108929108/525), (271164169/525), (8707377034/6825), (149501827997/47775), (1822794636944/238875), (4421093688779/238875), (181464106272914/4060875), (1308842996911559/12182625), (1045093478407892/4060875), (2878768890432653/4685625), (623522067315392278/426391875), (1479891318051055009/426391875), (80584385649576442024/9807013125), (190333597988265436541/9807013125)]]
[6, 6, [0, 1, 6, 24, 84, 270, 828, 2448, (49464/7), (139914/7), (390060/7), 153360, (32185080/77), (86944860/77), (3032105400/1001), (56568209760/7007), (149975710704/7007), (395650150074/7007), (2524489056036/17017), (46246789771632/119119), (120632789755080/119119), (28515506868756/10829), (5693918320825992/833833), (161997560869495968/9172163), (24591696614401104/539539), (153785725118311500/1310309)]]
[6, 7, [0, 1, 6, 25, 92, 313, (5098/5), (16053/5), (69224/7), (1046187/35), (3120298/35), (45977439/175), (1477179364/1925), (855770497/385), (160096437034/25025), (3205918344047/175175), (45635463761424/875875), (129320440952179/875875), (1241308566664506/2977975), (17457980084416811/14889875), (48958846175705124/14889875), (684467572218146071/74449375), (13363852457484047522/521145625), (81803915759606574967/1146520375), (26121500174992445410472/131849843125), (4257795719425376717709/7755873125)]]
[6, 8, [0, 1, 6, 26, 100, 358, (6148/5), (20468/5), (66728/5), 42758, (2029052/15), (10580652/25), (1083234616/825), (3334909436/825), (26533171336/2145), (403687377064/10725), (470308386256/4125), (18440248465558/53625), (55420395158468/53625), (99597271666372/32175), (9419872780750856/1018875), (420859059845592452/15283125), (1250630179360271992/15283125), (40787487804492951752/168114375), (24139133998714332368/33622875), (356473819934336529476/168114375)]]
[6, 9, [0, 1, 6, 27, 108, 405, 1458, 5103, 17496, 59049, 196830, 649539, 2125764, 6908733, 22320522, 71744535, 229582512, 731794257, 2324522934, 7360989291, 23245229340, 73222472421, 230127770466, 721764371007, 2259436291848, 7060738412025]]
[6, 10, [0, 1, 6, 28, 116, 454, (8524/5), (31224/5), (784024/35), (2773698/35), (1384196/5), (167753016/175), (6335672696/1925), (21620668108/1925), (73335496856/1925), (1733453258128/13475), (29134330415856/67375), (13942576687478/9625), (5538424391569596/1145375), (18437807721955352/1145375), (1162927480729955352/21762125), (1750937141541137948/9891875), (445545235369389408056/761674375), (16167073294961606643728/8378418125), (174890269322046406034864/27529088125), (4024484829154750738618452/192703616875)]]
[6, 11, [0, 1, 6, 29, 124, 505, 1970, 7525, 28120, 103865, (1135690/3), 1369653, (162072244/33), (578220161/33), (26645651858/429), (94105048105/429), (330744189680/429), (1159184600285/429), (68804271071870/7293), (719106831831755/21879), (832542437772860/7293), (8659463344144879/21879), (29948032830545774/21879), (1137639163133167681/240669), (90171210346207895128/5535387), (310365510859243397075/5535387)]]
[6, 12, [0, 1, 6, 30, 132, 558, (11268/5), (44748/5), (243000/7), (4670082/35), (17693388/35), (333285084/175), (1243395144/175), (924223716/35), (17053565688/175), (439334657784/1225), (8041166904528/6125), (29375517056238/6125), (363330230172228/20825), (6598155863092932/104125), (453785397574897512/1978375), (8202575780288288748/9891875), (206995018542033532536/69243125), (149093910483863261832/13848625), (2678410540526832731952/69243125), (9615237264163503892908/69243125)]]
[6, 13, [0, 1, 6, 31, 140, 613, (12778/5), (52623/5), (1478536/35), (1179519/7), (23152698/35), (64685967/25), (19270989684/1925), (74386147809/1925), (148124565738/1001), (99108155288397/175175), (1883133245846544/875875), (7148205060938259/875875), (551094451017666/17875), (20385575031763849/175175), (661951217419975188/1512875), (136803120908571358177/83208125), (3586672085004118532294/582456875), (147699940284492285132059/6407025625), (110284905472047822291368/1281405125), (293993622219779926368711/915289375)]]
[6, 14, [0, 1, 6, 32, 148, 670, 2876, 12256, (355384/7), (1467626/7), (17861380/21), (24119040/7), (289526840/21), (1157763100/21), (4587727960/21), (127223967680/147), (500486927152/147), (1968818145202/147), (130928797533388/2499), (1536664953207616/7497), (37900390050296440/47481), (442863228598492652/142443), (12028441131984138664/997101), (46681080347738863168/997101), (4153244526585325828816/22933323), (16069619003618245397300/22933323)]]
[6, 15, [0, 1, 6, 33, 156, 729, (16074/5), (70749/5), (301752/5), (1287549/5), (5384646/5), (112720113/25), (465332148/25), (1923467769/25), (102280575474/325), (418910747301/325), (8508864655152/1625), (2662240791789/125), (139847956989606/1625), (565752940062057/1625), (43251185382410052/30875), (871074717662046303/154375), (3492717394441338558/154375), (14018680054323786879/154375), (1289099581408204523784/3550625), (271511553373355663379/186875)]]
[6, 16, [0, 1, 6, 34, 164, 790, 3572, 16212, 71048, 312678, 1345220, 5809980, 24692600, 105305980, 443684360, 1875046120, 7848968208, 32944100998, 137210821092, 572842556332, 2376270786840, 9878362137364, 40842721771544, 169192718317336, 697620779210096, 2881488687879900]]
[7, 1, [0, 1, 7, (51/2), (133/2), (1135/8), (2121/8), (7219/16), (11461/16), (137979/128), (199005/128), (554565/256), (750915/256), (3970395/1024), (5141565/1024), (13082355/2048), (16388229/2048), (324035283/32768), (395637957/32768), (955788977/65536), (1143408695/65536), (5423928081/262144), (6381610807/262144), (14908881221/524288), (17300707203/524288), (159639366575/4194304)]]
[7, 2, [0, 1, 7, (53/2), (455/6), (4457/24), (49399/120), (613213/720), (1206001/720), (3650683/1152), (301438049/51840), (5395681043/518400), (104086138081/5702400), (2153062761919/68428800), (9509262882941/177914880), (159505578034493/1779148800), (3969317911123751/26687232000), (8026761756494069/32845824000), (169984956676016519/426995712000), (197856767950853597/307436912640), (150894644757794678471/146032533504000), (437776464033707372027/265513697280000), (22922898475306142508817/8761952010240000), (796111715104086101744923/192762944225280000), (250180480545551468966411/38552588845056000), (46969679144090434297580689/4626310661406720000)]]
[7, 3, [0, 1, 7, (55/2), (511/6), (5557/24), (69559/120), (987043/720), (447821/144), (39362767/5760), (759186049/51840), (15942249433/518400), (32920649291/518400), (32174620985/248832), (1618263272351/6220800), (6444456420101/12441600), (190754889452297/186624000), (5975292848638799/2985984000), (39496607946709189/10152345600), (6867700113185239097/913711104000), (250691499558914813249/17360510976000), (9584018625943576263323/347210219520000), (54708488546548242648143/1041630658560000), (41465365595684832703181/416652263424000), (391350400664027244785003/2083261317120000), (929841285215512130875799/2631487979520000)]]
[7, 4, [0, 1, 7, (57/2), (189/2), (2235/8), (6153/8), (32237/16), (81461/16), (1601811/128), (3852605/128), (18208135/256), (42407835/256), (390281775/1024), (888677085/1024), (4010931285/2048), (8981184613/2048), (319567894531/32768), (706382595333/32768), (3105951841507/65536), (6795358809535/65536), (59208731797461/262144), (128461984885047/262144), (555418390215627/524288), (1196736258711219/524288), (20565773090559575/4194304)]]
[7, 5, [0, 1, 7, (59/2), (623/6), (7901/24), (117607/120), (2008399/720), (5536609/720), (119092223/5760), (2826824801/51840), (73379273957/518400), (188037141659/518400), (5719016429033/6220800), (186702085497251/80870400), (930174221271541/161740800), (34516532373488437/2426112000), (1357824792140268259/38817792000), (56447257572926152133/659902464000), (2472602734985093501201/11878244352000), (5991212083926282876623/11878244352000), (22246058314307179250497/18274222080000), (2086562383263878193243361/712694661120000), (10003775168293176939757787/1425389322240000), (549935774328744223024277539/32783954411520000), (31459969884790377914901434893/786814905876480000)]]
[7, 6, [0, 1, 7, (61/2), (679/6), (9145/24), (29099/24), (532913/144), (1580477/144), (36643163/1152), (939268205/10368), (5272437091/20736), (160890462697/228096), (5302003414951/2737152), (187707496989049/35582976), (1014820029721405/71165952), (8178217933215731/213497856), (349515694092274757/3415965696), (15793461525653996291/58071416832), (752265045032994427889/1045285502976), (1982844124519629546545/1045285502976), (20830342855119347634499/4181142011904), (163595119820532674985739/12543426035712), (9393981609370990388161777/275955372785664), (24453593697423223216253741/275955372785664), (1523908507631385178409072075/6622928946855936)]]
[7, 7, [0, 1, 7, (63/2), (245/2), (3479/8), (58653/40), (380387/80), (1201529/80), (5942475/128), (90395249/640), (2712632993/6400), (88592772681/70400), (1042207431433/281600), (7908644255183/732160), (229224973796721/7321600), (3302883761506399/36608000), (151486171656708553/585728000), (7349093883505143567/9957376000), (8353934152737905011/3982950400), (10752376403627726623/1810432000), (6675686889995868457671/398295040000), (18783888624918655151977/398295040000), (1159543001433794328545173/8762490880000), (14929866903899687369623749/40307458048000), (1667673166392223447811793229/1612298321920000)]]
[7, 8, [0, 1, 7, (65/2), (791/6), (11777/24), (208999/120), (4289473/720), (2864285/144), (374776247/5760), (10872574529/51840), (345946919543/518400), (11989494022321/5702400), (89849281038731/13685760), (18107613376212193/889574400), (111550865656492433/1779148800), (394360251529721027/2052864000), (250064444949670084817/426995712000), (151836634234358105947/85399142400), (41323562270955025921793/7685922816000), (2366390092222704070807511/146032533504000), (142188359949262207297903297/2920650670080000), (1278055604216160161285508577/8761952010240000), (16804368656544713316458300171/38552588845056000), (250509651688960056476512140247/192762944225280000), (17885761472105645179135553145889/4626310661406720000)]]
[7, 9, [0, 1, 7, (67/2), (847/6), (13165/24), (48923/24), (1053371/144), (3695213/144), (101709203/1152), (3106462445/10368), (20825938309/20736), (69169193843/20736), (2733385694273/248832), (8942096001191/248832), (58143038498105/497664), (564273437961661/1492992), (29067706696912987/23887872), (93224430765208061/23887872), (5361539500256360321/429981696), (17077661810373943895/429981696), (216924148543752493009/1719926784), (2061311624064138433669/5159780352), (13025647782130722716639/10319560704), (41067936819020363937193/10319560704), (3101015478673378654354375/247669456896)]]
[7, 10, [0, 1, 7, (69/2), (301/2), (4867/8), (94269/40), (706661/80), (2592041/80), (74677167/640), (265445521/640), (9325835347/6400), (357270920529/70400), (4936999700581/281600), (16949221275319/281600), (115689215286939/563200), (1964863629868091/2816000), (106305417638627837/45056000), (6088566996711602379/765952000), (40879394105686933097/1531904000), (2599811217490217435699/29106176000), (15776397829458351619863/52920320000), (577809035539390776412631/582123520000), (42223545996064946354956877/12806717440000), (3219278541801771953132610999/294554501120000), (5011939680213547206888043883/138613882880000)]]
[7, 11, [0, 1, 7, (71/2), (959/6), (16085/24), (64715/24), (1514615/144), (5785805/144), (173786755/1152), (5798864845/10368), (42528188273/20736), (1701022610401/228096), (73658087645203/2737152), (3434561412964537/35582976), (24500774479492595/71165952), (260982137526949075/213497856), (14763283887860733685/3415965696), (884201542695656768195/58071416832), (55882624365408826961075/1045285502976), (195660240746259081614585/1045285502976), (2732759809122751100547719/4181142011904), (28559911587628949873672939/12543426035712), (2183903002536519948113354567/275955372785664), (10250105230264610272568062379/373351386710016), (14480421553803237747379888353925/152327365777686528)]]
[7, 12, [0, 1, 7, (73/2), (1015/6), (17617/24), (366919/120), (8910553/720), (35328721/720), (220542827/1152), (38243013889/51840), (1458632363023/518400), (5517382261331/518400), (248664736104629/6220800), (185679888399139/1244160), (6896353108506791/12441600), (382498270877997737/186624000), (22538984848645542239/2985984000), (1406247250086303409241/50761728000), (18521376622966110993259/182742220800), (6419486896158003076289129/17360510976000), (467223795276733352180329103/347210219520000), (5089254360510495567108501983/1041630658560000), (36878729671158753081507287587/2083261317120000), (5334642634260704042807728883/83330452684800), (11554636606289344094965451379581/49998271610880000)]]
[7, 13, [0, 1, 7, (75/2), (357/2), (6399/8), (137613/40), (1152967/80), (946181/16), (153024903/640), (611033489/640), (24170471813/6400), (1042971191961/70400), (3251821864989/56320), (818862291040251/3660800), (6314441242871661/7321600), (121185794068599839/36608000), (7415319451066726313/585728000), (5652002399812189587/117145600), (214778315060337843643/1171456000), (15463894132958473185391/22257664000), (106295648666252569081287/40468480000), (4410363186345462448166379/445153280000), (73055730601689763893378711/1958674432000), (1372535635253895379143769389/9793372160000), (41191563061804433109225724961/78346977280000)]]
[7, 14, [0, 1, 7, (77/2), (1127/6), (20825/24), (92267/24), (2395169/144), (10145597/144), (339278107/1152), (12601708525/10368), (103140474899/20736), (418482686363/20736), (20256978587573/248832), (81212695163831/248832), (648408095615875/497664), (7729637727624029/1492992), (489837704347236203/23887872), (32863324397222955853/406093824), (2328507996204120584623/7309688832), (173649153187332356716525/138884087808), (2720641322423449601442007/555536351232), (1876099944582075619401071/98035826688), (248829861393139493676467447/3333218107392), (22281351223036540336938197437/76664016470016), (2078926627407437789490307812475/1839936395280384)]]
[7, 15, [0, 1, 7, (79/2), (1183/6), (22501/24), (512407/120), (13712299/720), (59828929/720), (2064278383/5760), (79065192001/51840), (3340232161057/518400), (13985381084459/518400), (699139456581473/6220800), (37619767933704371/80870400), (310284156000478841/161740800), (19100884662170318837/2426112000), (96209934941301235343/2985984000), (5099218441253724310069/38817792000), (373391400732743406224413/698720256000), (28772730408760809554224861/13275684864000), (2329740097037963082358728127/265513697280000), (28225197464922691681161103027/796541091840000), (227638098029276572118478960629/1593082183680000), (21068852937001593264830513813033/36640890224640000), (2032325422241421169994819390699351/879381365391360000)]]
[7, 16, [0, 1, 7, (81/2), (413/2), (8075/8), (37737/8), (346453/16), (1554037/16), (55224243/128), (241868925/128), (2105792271/256), (9079855227/256), (155957034207/1024), (665087599101/1024), (5655712693725/2048), (23922135761637/2048), (1615317399925059/32768), (6789197449065861/32768), (56970643702430891/65536), (238243502892055775/65536), (3979662101004455109/262144), (16574138218759721303/262144), (137896366098626022499/524288), (572340882247719001587/524288), (18986196919202141883575/4194304)]]
[8, 1, [0, 1, 8, 33, 96, 225, 456, 833, 1408, 2241, 3400, 4961, 7008, 9633, 12936, 17025, 22016, 28033, 35208, 43681, 53600, 65121, 78408, 93633, 110976, 130625]]
[8, 2, [0, 1, 8, 34, (320/3), (844/3), (9952/15), (65128/45), (134144/45), (52880/9), (4529792/405), (41915168/2025), (833598464/22275), (4433598016/66825), (20097892864/173745), (172696099456/868725), (4396252725248/13030875), (7379009346304/13030875), (12264980436992/13030875), (36376417996288/23455575), (5649680029302784/2228279625), (45856957155079168/11141398125), (221898351913459712/33424194375), (3914152579889063936/367666138125), (1248641623541940224/73533227625), (29728123597044084736/1102998414375)]]
[8, 3, [0, 1, 8, 35, (352/3), (1019/3), (13432/15), (99583/45), (328576/63), (3734123/315), (10604392/405), (801029581/14175), (1696028128/14175), (2120264497/8505), (21788143912/42525), (309780347833/297675), (9341508114944/4465125), (2658695672851/637875), (25012154861672/3036285), (11043604683037463/683164125), (409129723565243104/12980118375), (3965686781796163163/64900591875), (160601357177420883064/1362912429375), (61647752154444083713/272582485875), (84145364791427355776/194701775625), (197833317675880897501/240513958125)]]
[8, 4, [0, 1, 8, 36, 128, 400, 1152, 3136, 8192, 20736, 51200, 123904, 294912, 692224, 1605632, 3686400, 8388608, 18939904, 42467328, 94633984, 209715200, 462422016, 1015021568, 2218786816, 4831838208, 10485760000]]
[8, 5, [0, 1, 8, 37, (416/3), (1387/3), (21496/15), (190009/45), (3777152/315), (10427467/315), (253391576/2835), (3359746379/14175), (8778241312/14175), (67952678309/42525), (2255378482312/552825), (39939982559843/3869775), (1503593563692544/58046625), (288253497987269/4465125), (157783816704542216/986792625), (3497816304301559069/8881133625), (8573036511410319328/8881133625), (104591480630359615381/44405668125), (5337576013533294570248/932519030625), (12923042198381684913277/932519030625), (42188563479022491463808/1261643394375), (5175655137585063649965301/64343813113125)]]
[8, 6, [0, 1, 8, 38, (448/3), (1580/3), (5216/3), (49304/9), (1051648/63), (3122416/63), (81768320/567), (33432160/81), (7268910080/6237), (60874793920/18711), (2187923310080/243243), (41989330720640/1702701), (342861266223104/5108103), (927238586083072/5108103), (6055679691917312/12405393), (1020764053397944832/781539759), (247167483131740160/71049069), (554778557397486592/60118443), (400271101589930467328/16412334939), (11597084453547635283968/180535684329), (30451661210517197029376/180535684329), (4881615946415808819200/11053205163)]]
[8, 7, [0, 1, 8, 39, 160, 593, (10344/5), (34547/5), (783232/35), (495207/7), (7683544/35), (117395401/175), (3897327648/1925), (11637664309/1925), (89551626088/5005), (9204224686593/175175), (10326564701696/67375), (389270534591779/875875), (19089359870257944/14889875), (10961470711751713/2977975), (156702299537598688/14889875), (202878361239249741/6768125), (44343161983063004296/521145625), (1380238451719763731573/5732601875), (3582945899430507618432/5273993725), (252076273222136190936853/131849843125)]]
[8, 8, [0, 1, 8, 40, (512/3), (1984/3), (36352/15), (383488/45), (262144/9), (4378624/45), (129400832/405), (2093907968/2025), (73687629824/22275), (28006678528/2673), (28591876210688/868725), (89155579150336/868725), (4144269778485248/13030875), (12770804387282944/13030875), (7832789705555968/2606175), (1076153709995491328/117277875), (62185511265966751744/2228279625), (85658894738955173888/1012854375), (8539116028634303823872/33424194375), (56581978887292608053248/73533227625), (849845652062936315723776/367666138125), (7639683118538049282113536/1102998414375)]]
[8, 9, [0, 1, 8, 41, (544/3), (2195/3), (8408/3), (92897/9), (333184/9), (1169257/9), (36341960/81), (123783385/81), (417101920/81), (4176355235/243), (13831816600/243), (45491092315/243), (446244795904/729), (1451381890457/729), (4699206405704/729), (136358758749833/6561), (438049933072480/6561), (1402448801977489/6561), (13430146823788376/19683), (42749807407497067/19683), (135740819642790016/19683), (1289985619645210825/59049)]]
[8, 10, [0, 1, 8, 42, 192, 804, (16032/5), (61576/5), (1614848/35), (5925168/35), (3059328/5), (381919584/175), (14833769472/1925), (51900333888/1925), (180276361728/1925), (4354128819072/13475), (74707736788992/67375), (36437187049728/9625), (14740797728913408/1145375), (49911718246471168/1145375), (3200045314465316864/21762125), (53816222963078243328/108810625), (1263525787964402884608/761674375), (46492594833427858900992/8378418125), (509808714602480309895168/27529088125), (11882850479094194936983552/192703616875)]]
[8, 11, [0, 1, 8, 43, (608/3), (2635/3), (10904/3), (130571/9), (509056/9), (1945337/9), (65959240/81), (245355755/81), (9943914080/891), (108951967225/2673), (5137554878120/34749), (18515876957815/34749), (199164714110464/104247), (710606296663127/104247), (42928651911961784/1772199), (1367665004931889877/15949791), (4825795488729222880/15949791), (16974633249742477799/15949791), (10508872469700758888/2814669), (6876395197596171045421/526343103), (552196426994781972113536/12105891369), (5771380381970275795588075/36317674107)]]
[8, 12, [0, 1, 8, 44, (640/3), (2864/3), (61312/15), (760768/45), (21536768/315), (17088256/63), (3009501184/2835), (58176295936/14175), (222880104448/14175), (2540106862592/42525), (383473057792/1701), (251716282236928/297675), (14093131578343424/4465125), (52355496591818752/4465125), (3293842814716608512/75907125), (21860012600289132544/136632825), (7633365959810045968384/12980118375), (139868803741268147437568/64900591875), (10736991539290803099664384/1362912429375), (39151299102541683372326912/1362912429375), (28492348327518218456399872/272582485875), (1551908509329091693685768192/4088737288125)]]
[8, 13, [0, 1, 8, 45, 224, 1033, (22824/5), (97577/5), (571520/7), (11737107/35), (47581784/35), (136177013/25), (41646888288/1925), (32815556441/385), (8350946378312/25025), (227507801861763/175175), (4406368073763328/875875), (16991191157896259/875875), (1865103989184648/25025), (249898213773301447/875875), (18123009696687693536/16641625), (344870313403402674117/83208125), (9165623581068641023192/582456875), (76375535608216128176777/1281405125), (1443511190541887193580416/6407025625), (777940030197334866097711/915289375)]]
[8, 14, [0, 1, 8, 46, (704/3), (3340/3), (15200/3), (201080/9), (6077440/63), (25783280/63), (972023680/567), (4026312224/567), (16536558592/567), (202178230592/1701), (818952833536/1701), (23089277932160/11907), (277714977751040/35721), (1108607162026240/35721), (74965022000957440/607257), (2674496629064035840/5465313), (200862235702804398080/103840947), (791760997612155292672/103840947), (65387585277521735376896/2180659887), (256555037035254287091712/2180659887), (23107242755644033088094208/50155177401), (14259968870089456548352000/7919238537)]]
[8, 15, [0, 1, 8, 47, (736/3), (3587/3), (83896/15), (1142659/45), (5081216/45), (22221101/45), (863732968/405), (18454175047/2025), (78201190816/2025), (986840258747/6075), (53642418697336/78975), (223086661139857/78975), (13854237496019456/1184625), (57121617504477553/1184625), (234694323618869512/1184625), (8650195657579947703/10661625), (671192505343039879904/202570875), (13668913822737505236583/1012854375), (166639929499598264677352/3038563125), (675697460023041650074363/3038563125), (62896355357545734514281344/69886951875), (762243226481393842341247049/209660855625)]]
[8, 16, [0, 1, 8, 48, 256, 1280, 6144, 28672, 131072, 589824, 2621440, 11534336, 50331648, 218103808, 939524096, 4026531840, 17179869184, 73014444032, 309237645312, 1305670057984, 5497558138880, 23089744183296, 96757023244288, 404620279021568, 1688849860263936, 7036874417766400]]

0 件のコメント:

コメントを投稿

注: コメントを投稿できるのは、このブログのメンバーだけです。