隣り合う階乗の和(5)
1 / ((0 + 2)^(k - 1) 0!) + 1 / ((1 + 2)^(k - 1) 1!) + 1 / ((2 + 2)^(k - 1) 2!) + … の和を求めてみた。
require 'bigdecimal'
def f(n)
return 1 if n == 0
(1..n).inject(:*)
end
# 階乗の和で表現
def g(k, n)
return f(n - 1) if k == 1
return f(n - 1) + f(n) if k == 2
return f(n - 1) + f(n) + f(n + 1) if k == 3
return f(n - 1) + f(n) + f(n + 2) if k == 4
return f(n - 1) + f(n) + f(n + 1) - 2 * f(n + 2) + f(n + 3) if k == 5
end
def h(k, n)
(1..n).inject(0){|s, i| s += 1r / g(k, i)}
end
def i(k, n)
(1..n).map{|i| g(k, i)}
end
n = 40
(1..5).each{|k| p i(k, n)}
(1..5).each{|k|
(1..n).each{|i|
p BigDecimal(h(k, i), 40).to_s("F")
}
}
出力結果
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[2, 3, 8, 30, 144, 840, 5760, 45360, 403200, 3991680, 43545600, 518918400, 6706022400, 93405312000, 1394852659200, 22230464256000, 376610217984000, 6758061133824000, 128047474114560000, 2554547108585472000, 53523844179886080000, 1175091669949317120000, 26976017466662584320000, 646300418472124416000000, 16131658445064225423360000, 418802671169936621568000000, 11292160911544957796352000000, 315777214062132212662272000000, 9146650338351415815045120000000, 274094621805930760590852096000000, 8488091513990113876361871360000000, 271353675587871452984943575040000000, 8946448455745580025685412413440000000, 303916116658416027343136804044800000000, 10628380765425749070514269947166720000000, 382326474756287362397666099488358400000000, 14135746418016246263783979029731737600000000, 536786370557827456806323203681655193600000000, 20920904698664044470400288964002971648000000000, 836313165329095177704251551336018791628800000000]
[4, 9, 32, 150, 864, 5880, 46080, 408240, 4032000, 43908480, 522547200, 6745939200, 93884313600, 1401079680000, 22317642547200, 377917892352000, 6778983923712000, 128403161542656000, 2560949482291200000, 53645489280294912000, 1177524571957493760000, 27027108408834293760000, 647424419199902023680000, 16157510461803110400000000, 419423119571669861007360000, 11307672121588288782336000000, 316180505523258818297856000000, 9157539207801834167205888000000, 274399510150542474451353600000000, 8496933275983853578316414976000000, 271618928447683644043579883520000000, 8954671294399757948503137976320000000, 304179247495349720873304022056960000000, 10637064083044560957009788141568000000000, 382621707555326966538513718098001920000000, 14146079565982632408713645681069260800000000, 537158363884617358023791203129806028800000000, 20934668451755270815446604943584552550400000000, 836836187946561778816011558560118865920000000000, 34288839778492902285874313604776770456780800000000]
[8, 27, 128, 750, 5184, 41160, 368640, 3674160, 40320000, 482993280, 6270566400, 87697209600, 1314380390400, 21016195200000, 357082280755200, 6424604169984000, 122021710626816000, 2439660069310464000, 51218989645824000000, 1126555274886193152000, 25905540583064862720000, 621623493403188756480000, 15538186060797648568320000, 403937761545077760000000000, 10905001108863416386191360000, 305307147282883797123072000000, 8853054154651246912339968000000, 265568637026253190848970752000000, 8231985304516274233540608000000000, 263404931555499460927808864256000000, 8691805710325876609394556272640000000, 295504152715192012300603553218560000000, 10342094414841890509692336749936640000000, 372297242906559633495342584954880000000000, 13774381471991770795386493851528069120000000, 523404943941357399122404890199562649600000000, 20412017827615459604904065718932629094400000000, 816452069618455561802417592799797549465600000000, 33473447517862471152640462342404754636800000000000, 1405842430918208993720846857795847588728012800000000]
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