200830

Ruby


88888

意外なことに88888 が見つからなかった。

(1..9).to_a.permutation{|i|
  a, b = i[0..4].join.to_i, i[5..-1].join.to_i
  if (a - b) % 11111 == 0
    puts "#{a} - #{b} = #{a - b}"
  elsif (a + b) % 11111 == 0
    puts "#{a} + #{b} = #{a + b}"
  end
}

出力結果

13579 - 2468 = 11111

13597 - 2486 = 11111

13759 - 2648 = 11111

13795 - 2684 = 11111

13957 - 2846 = 11111

13975 - 2864 = 11111

15379 - 4268 = 11111

15397 - 4286 = 11111

15739 - 4628 = 11111

15793 - 4682 = 11111

15937 - 4826 = 11111

15973 - 4862 = 11111

17359 - 6248 = 11111

17395 - 6284 = 11111

17539 - 6428 = 11111

17593 - 6482 = 11111

17935 - 6824 = 11111

17953 - 6842 = 11111

19357 - 8246 = 11111

19375 - 8264 = 11111

19537 - 8426 = 11111

19573 - 8462 = 11111

19735 - 8624 = 11111

19753 - 8642 = 11111

25718 - 3496 = 22222

25871 - 3649 = 22222

27158 - 4936 = 22222

27185 - 4963 = 22222

28571 - 6349 = 22222

28715 - 6493 = 22222

31478 - 9256 = 22222

31487 - 9265 = 22222

31748 - 9526 = 22222

31784 - 9562 = 22222

31847 - 9625 = 22222

31874 - 9652 = 22222

41268 - 7935 = 33333

41286 - 7953 = 33333

46279 - 1835 = 44444

46297 - 1853 = 44444

46819 - 2375 = 44444

46981 - 2537 = 44444

47629 - 3185 = 44444

47962 - 3518 = 44444

48169 - 3725 = 44444

48196 - 3752 = 44444

49627 - 5183 = 44444

49681 - 5237 = 44444

49762 - 5318 = 44444

49816 - 5372 = 44444

51238 - 6794 = 44444

51427 - 6983 = 44444

52138 - 7694 = 44444

53416 - 8972 = 44444

54127 - 9683 = 44444

54316 - 9872 = 44444

56789 - 1234 = 55555

56798 - 1243 = 55555

56834 - 1279 = 55555

56879 - 1324 = 55555

56897 - 1342 = 55555

56942 - 1387 = 55555

56978 - 1423 = 55555

56987 - 1432 = 55555

57239 - 1684 = 55555

57248 - 1693 = 55555

57689 - 2134 = 55555

57698 - 2143 = 55555

57869 - 2314 = 55555

57896 - 2341 = 55555

57941 - 2386 = 55555

57968 - 2413 = 55555

57986 - 2431 = 55555

58319 - 2764 = 55555

58346 - 2791 = 55555

58679 - 3124 = 55555

58697 - 3142 = 55555

58724 - 3169 = 55555

58769 - 3214 = 55555

58796 - 3241 = 55555

58967 - 3412 = 55555

58976 - 3421 = 55555

59417 - 3862 = 55555

59426 - 3871 = 55555

59678 - 4123 = 55555

59687 - 4132 = 55555

59723 - 4168 = 55555

59768 - 4213 = 55555

59786 - 4231 = 55555

59831 - 4276 = 55555

59867 - 4312 = 55555

59876 - 4321 = 55555

61289 - 5734 = 55555

61298 - 5743 = 55555

61379 - 5824 = 55555

61397 - 5842 = 55555

61478 - 5923 = 55555

61487 - 5932 = 55555

69153 - 2487 = 66666

69513 - 2847 = 66666

71358 - 4692 = 66666

71529 - 4863 = 66666

71934 - 5268 = 66666

73158 - 6492 = 66666

73194 - 6528 = 66666

73491 - 6825 = 66666

74931 - 8265 = 66666

75129 - 8463 = 66666

81256 - 3479 = 77777

81472 - 3695 = 77777

81526 - 3749 = 77777

81742 - 3965 = 77777

82156 - 4379 = 77777

82516 - 4739 = 77777

84172 - 6395 = 77777

84712 - 6935 = 77777

85126 - 7349 = 77777

85216 - 7439 = 77777

87142 - 9365 = 77777

87412 - 9635 = 77777

91234 + 8765 = 99999

91235 + 8764 = 99999

91243 + 8756 = 99999

91246 + 8753 = 99999

91253 + 8746 = 99999

91256 + 8743 = 99999

91264 + 8735 = 99999

91265 + 8734 = 99999

91324 + 8675 = 99999

91325 + 8674 = 99999

91342 + 8657 = 99999

91347 + 8652 = 99999

91352 + 8647 = 99999

91357 + 8642 = 99999

91374 + 8625 = 99999

91375 + 8624 = 99999

91423 + 8576 = 99999

91426 + 8573 = 99999

91432 + 8567 = 99999

91437 + 8562 = 99999

91462 + 8537 = 99999

91467 + 8532 = 99999

91473 + 8526 = 99999

91476 + 8523 = 99999

91523 + 8476 = 99999

91526 + 8473 = 99999

91532 + 8467 = 99999

91537 + 8462 = 99999

91562 + 8437 = 99999

91567 + 8432 = 99999

91573 + 8426 = 99999

91576 + 8423 = 99999

91624 + 8375 = 99999

91625 + 8374 = 99999

91642 + 8357 = 99999

91647 + 8352 = 99999

91652 + 8347 = 99999

91657 + 8342 = 99999

91674 + 8325 = 99999

91675 + 8324 = 99999

91734 + 8265 = 99999

91735 + 8264 = 99999

91743 + 8256 = 99999

91746 + 8253 = 99999

91753 + 8246 = 99999

91756 + 8243 = 99999

91764 + 8235 = 99999

91765 + 8234 = 99999

92134 + 7865 = 99999

92135 + 7864 = 99999

92143 + 7856 = 99999

92146 + 7853 = 99999

92153 + 7846 = 99999

92156 + 7843 = 99999

92164 + 7835 = 99999

92165 + 7834 = 99999

92314 + 7685 = 99999

92315 + 7684 = 99999

92341 + 7658 = 99999

92348 + 7651 = 99999

92351 + 7648 = 99999

92358 + 7641 = 99999

92384 + 7615 = 99999

92385 + 7614 = 99999

92413 + 7586 = 99999

92416 + 7583 = 99999

92431 + 7568 = 99999

92438 + 7561 = 99999

92461 + 7538 = 99999

92468 + 7531 = 99999

92483 + 7516 = 99999

92486 + 7513 = 99999

92513 + 7486 = 99999

92516 + 7483 = 99999

92531 + 7468 = 99999

92538 + 7461 = 99999

92561 + 7438 = 99999

92568 + 7431 = 99999

92583 + 7416 = 99999

92586 + 7413 = 99999

92614 + 7385 = 99999

92615 + 7384 = 99999

92641 + 7358 = 99999

92648 + 7351 = 99999

92651 + 7348 = 99999

92658 + 7341 = 99999

92684 + 7315 = 99999

92685 + 7314 = 99999

92834 + 7165 = 99999

92835 + 7164 = 99999

92843 + 7156 = 99999

92846 + 7153 = 99999

92853 + 7146 = 99999

92856 + 7143 = 99999

92864 + 7135 = 99999

92865 + 7134 = 99999

93124 + 6875 = 99999

93125 + 6874 = 99999

93142 + 6857 = 99999

93147 + 6852 = 99999

93152 + 6847 = 99999

93157 + 6842 = 99999

93174 + 6825 = 99999

93175 + 6824 = 99999

93214 + 6785 = 99999

93215 + 6784 = 99999

93241 + 6758 = 99999

93248 + 6751 = 99999

93251 + 6748 = 99999

93258 + 6741 = 99999

93284 + 6715 = 99999

93285 + 6714 = 99999

93412 + 6587 = 99999

93417 + 6582 = 99999

93421 + 6578 = 99999

93428 + 6571 = 99999

93471 + 6528 = 99999

93478 + 6521 = 99999

93482 + 6517 = 99999

93487 + 6512 = 99999

93512 + 6487 = 99999

93517 + 6482 = 99999

93521 + 6478 = 99999

93528 + 6471 = 99999

93571 + 6428 = 99999

93578 + 6421 = 99999

93582 + 6417 = 99999

93587 + 6412 = 99999

93714 + 6285 = 99999

93715 + 6284 = 99999

93741 + 6258 = 99999

93748 + 6251 = 99999

93751 + 6248 = 99999

93758 + 6241 = 99999

93784 + 6215 = 99999

93785 + 6214 = 99999

93824 + 6175 = 99999

93825 + 6174 = 99999

93842 + 6157 = 99999

93847 + 6152 = 99999

93852 + 6147 = 99999

93857 + 6142 = 99999

93874 + 6125 = 99999

93875 + 6124 = 99999

94123 + 5876 = 99999

94126 + 5873 = 99999

94132 + 5867 = 99999

94137 + 5862 = 99999

94162 + 5837 = 99999

94167 + 5832 = 99999

94173 + 5826 = 99999

94176 + 5823 = 99999

94213 + 5786 = 99999

94216 + 5783 = 99999

94231 + 5768 = 99999

94238 + 5761 = 99999

94261 + 5738 = 99999

94268 + 5731 = 99999

94283 + 5716 = 99999

94286 + 5713 = 99999

94312 + 5687 = 99999

94317 + 5682 = 99999

94321 + 5678 = 99999

94328 + 5671 = 99999

94371 + 5628 = 99999

94378 + 5621 = 99999

94382 + 5617 = 99999

94387 + 5612 = 99999

94612 + 5387 = 99999

94617 + 5382 = 99999

94621 + 5378 = 99999

94628 + 5371 = 99999

94671 + 5328 = 99999

94678 + 5321 = 99999

94682 + 5317 = 99999

94687 + 5312 = 99999

94713 + 5286 = 99999

94716 + 5283 = 99999

94731 + 5268 = 99999

94738 + 5261 = 99999

94761 + 5238 = 99999

94768 + 5231 = 99999

94783 + 5216 = 99999

94786 + 5213 = 99999

94823 + 5176 = 99999

94826 + 5173 = 99999

94832 + 5167 = 99999

94837 + 5162 = 99999

94862 + 5137 = 99999

94867 + 5132 = 99999

94873 + 5126 = 99999

94876 + 5123 = 99999

95123 + 4876 = 99999

95126 + 4873 = 99999

95132 + 4867 = 99999

95137 + 4862 = 99999

95162 + 4837 = 99999

95167 + 4832 = 99999

95173 + 4826 = 99999

95176 + 4823 = 99999

95213 + 4786 = 99999

95216 + 4783 = 99999

95231 + 4768 = 99999

95238 + 4761 = 99999

95261 + 4738 = 99999

95268 + 4731 = 99999

95283 + 4716 = 99999

95286 + 4713 = 99999

95312 + 4687 = 99999

95317 + 4682 = 99999

95321 + 4678 = 99999

95328 + 4671 = 99999

95371 + 4628 = 99999

95378 + 4621 = 99999

95382 + 4617 = 99999

95387 + 4612 = 99999

95612 + 4387 = 99999

95617 + 4382 = 99999

95621 + 4378 = 99999

95628 + 4371 = 99999

95671 + 4328 = 99999

95678 + 4321 = 99999

95682 + 4317 = 99999

95687 + 4312 = 99999

95713 + 4286 = 99999

95716 + 4283 = 99999

95731 + 4268 = 99999

95738 + 4261 = 99999

95761 + 4238 = 99999

95768 + 4231 = 99999

95783 + 4216 = 99999

95786 + 4213 = 99999

95823 + 4176 = 99999

95826 + 4173 = 99999

95832 + 4167 = 99999

95837 + 4162 = 99999

95862 + 4137 = 99999

95867 + 4132 = 99999

95873 + 4126 = 99999

95876 + 4123 = 99999

96124 + 3875 = 99999

96125 + 3874 = 99999

96142 + 3857 = 99999

96147 + 3852 = 99999

96152 + 3847 = 99999

96157 + 3842 = 99999

96174 + 3825 = 99999

96175 + 3824 = 99999

96214 + 3785 = 99999

96215 + 3784 = 99999

96241 + 3758 = 99999

96248 + 3751 = 99999

96251 + 3748 = 99999

96258 + 3741 = 99999

96284 + 3715 = 99999

96285 + 3714 = 99999

96412 + 3587 = 99999

96417 + 3582 = 99999

96421 + 3578 = 99999

96428 + 3571 = 99999

96471 + 3528 = 99999

96478 + 3521 = 99999

96482 + 3517 = 99999

96487 + 3512 = 99999

96512 + 3487 = 99999

96517 + 3482 = 99999

96521 + 3478 = 99999

96528 + 3471 = 99999

96571 + 3428 = 99999

96578 + 3421 = 99999

96582 + 3417 = 99999

96587 + 3412 = 99999

96714 + 3285 = 99999

96715 + 3284 = 99999

96741 + 3258 = 99999

96748 + 3251 = 99999

96751 + 3248 = 99999

96758 + 3241 = 99999

96784 + 3215 = 99999

96785 + 3214 = 99999

96824 + 3175 = 99999

96825 + 3174 = 99999

96842 + 3157 = 99999

96847 + 3152 = 99999

96852 + 3147 = 99999

96857 + 3142 = 99999

96874 + 3125 = 99999

96875 + 3124 = 99999

97134 + 2865 = 99999

97135 + 2864 = 99999

97143 + 2856 = 99999

97146 + 2853 = 99999

97153 + 2846 = 99999

97156 + 2843 = 99999

97164 + 2835 = 99999

97165 + 2834 = 99999

97314 + 2685 = 99999

97315 + 2684 = 99999

97341 + 2658 = 99999

97348 + 2651 = 99999

97351 + 2648 = 99999

97358 + 2641 = 99999

97384 + 2615 = 99999

97385 + 2614 = 99999

97413 + 2586 = 99999

97416 + 2583 = 99999

97431 + 2568 = 99999

97438 + 2561 = 99999

97461 + 2538 = 99999

97468 + 2531 = 99999

97483 + 2516 = 99999

97486 + 2513 = 99999

97513 + 2486 = 99999

97516 + 2483 = 99999

97531 + 2468 = 99999

97538 + 2461 = 99999

97561 + 2438 = 99999

97568 + 2431 = 99999

97583 + 2416 = 99999

97586 + 2413 = 99999

97614 + 2385 = 99999

97615 + 2384 = 99999

97641 + 2358 = 99999

97648 + 2351 = 99999

97651 + 2348 = 99999

97658 + 2341 = 99999

97684 + 2315 = 99999

97685 + 2314 = 99999

97834 + 2165 = 99999

97835 + 2164 = 99999

97843 + 2156 = 99999

97846 + 2153 = 99999

97853 + 2146 = 99999

97856 + 2143 = 99999

97864 + 2135 = 99999

97865 + 2134 = 99999

98234 + 1765 = 99999

98235 + 1764 = 99999

98243 + 1756 = 99999

98246 + 1753 = 99999

98253 + 1746 = 99999

98256 + 1743 = 99999

98264 + 1735 = 99999

98265 + 1734 = 99999

98324 + 1675 = 99999

98325 + 1674 = 99999

98342 + 1657 = 99999

98347 + 1652 = 99999

98352 + 1647 = 99999

98357 + 1642 = 99999

98374 + 1625 = 99999

98375 + 1624 = 99999

98423 + 1576 = 99999

98426 + 1573 = 99999

98432 + 1567 = 99999

98437 + 1562 = 99999

98462 + 1537 = 99999

98467 + 1532 = 99999

98473 + 1526 = 99999

98476 + 1523 = 99999

98523 + 1476 = 99999

98526 + 1473 = 99999

98532 + 1467 = 99999

98537 + 1462 = 99999

98562 + 1437 = 99999

98567 + 1432 = 99999

98573 + 1426 = 99999

98576 + 1423 = 99999

98624 + 1375 = 99999

98625 + 1374 = 99999

98642 + 1357 = 99999

98647 + 1352 = 99999

98652 + 1347 = 99999

98657 + 1342 = 99999

98674 + 1325 = 99999

98675 + 1324 = 99999

98734 + 1265 = 99999

98735 + 1264 = 99999

98743 + 1256 = 99999

98746 + 1253 = 99999

98753 + 1246 = 99999

98756 + 1243 = 99999

98764 + 1235 = 99999

98765 + 1234 = 99999

200827

Ruby


A336940

60 = 2^2 * 3^1 * 5^1

の約数は、

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

であるが、このうち奇数のものは、

1, 3, 5, 15

である。これらは、

15 = 3^1 * 5^1

の約数である。

この考え方を使って、

n! の約数のうち奇数となるものの個数を求めてみた。

require 'prime'

def A(n)
  h = {}
  Prime.each(n * n){|i| h[i] = 1}
  ary0 = []
  ary1 = [1]
  (1..n * n).each{|i|
    i.prime_division.each{|j| h[j[0]] += j[1]}
    ary0 << h[2]
    ary1 << h.values.inject(:*) / h[2]
  }
  p ary0
  p ary1
end

A(15)

出力結果

[1, 2, 2, 4, 4, 5, 5, 8, 8, 9, 9, 11, 11, 12, 12, 16, 16, 17, 17, 19, 19, 20, 20, 23, 23, 24, 24, 26, 26, 27, 27, 32, 32, 33, 33, 35, 35, 36, 36, 39, 39, 40, 40, 42, 42, 43, 43, 47, 47, 48, 48, 50, 50, 51, 51, 54, 54, 55, 55, 57, 57, 58, 58, 64, 64, 65, 65, 67, 67, 68, 68, 71, 71, 72, 72, 74, 74, 75, 75, 79, 79, 80, 80, 82, 82, 83, 83, 86, 86, 87, 87, 89, 89, 90, 90, 95, 95, 96, 96, 98, 98, 99, 99, 102, 102, 103, 103, 105, 105, 106, 106, 110, 110, 111, 111, 113, 113, 114, 114, 117, 117, 118, 118, 120, 120, 121, 121, 128, 128, 129, 129, 131, 131, 132, 132, 135, 135, 136, 136, 138, 138, 139, 139, 143, 143, 144, 144, 146, 146, 147, 147, 150, 150, 151, 151, 153, 153, 154, 154, 159, 159, 160, 160, 162, 162, 163, 163, 166, 166, 167, 167, 169, 169, 170, 170, 174, 174, 175, 175, 177, 177, 178, 178, 181, 181, 182, 182, 184, 184, 185, 185, 191, 191, 192, 192, 194, 194, 195, 195, 198, 198, 199, 199, 201, 201, 202, 202, 206, 206, 207, 207, 209, 209, 210, 210, 213, 213, 214, 214, 216, 216, 217, 217, 222, 222]

[1, 1, 1, 2, 2, 4, 6, 12, 12, 20, 30, 60, 72, 144, 216, 336, 336, 672, 864, 1728, 2160, 3200, 4800, 9600, 10560, 14784, 22176, 28224, 35280, 70560, 86400, 172800, 172800, 245760, 368640, 497664, 559872, 1119744, 1679616, 2363904, 2626560, 5253120, 6451200, 12902400, 16128000, 19514880, 29272320, 58544640, 61205760, 78693120, 93000960, 129392640, 161740800, 323481600, 363916800, 470292480, 522547200, 722534400, 1083801600, 2167603200, 2405376000, 4810752000, 7216128000, 8485171200, 8485171200, 10861019136, 13079937024, 26159874048, 32699842560, 44962283520, 52115374080, 104230748160, 110547763200, 221095526400, 331643289600, 381250437120, 476563046400, 590030438400, 707490201600, 1414980403200, 1489453056000, 1650475008000, 2475712512000, 4951425024000, 5462360064000, 6882573680640, 10323860520960, 14092888965120, 15854500085760, 31709000171520, 34764020121600, 42568187904000, 53210234880000, 72523579392000, 108785369088000, 136476190310400, 139443064012800, 278886128025600, 316070945095680, 366134191718400, 397971947520000, 795943895040000, 947552256000000, 1895104512000000, 2131992576000000, 2394654061363200, 3591981092044800, 7183962184089600, 7606548194918400, 15213096389836800, 17378037029928960, 23599803373977600, 24910903561420800, 49821807122841600, 59182267855011840, 73649044441792512, 92061305552240640, 105943565913292800, 158915348869939200, 191176359542784000, 201417950232576000, 238039395729408000, 357059093594112000, 484147923517440000, 605184904396800000, 667790239334400000, 724552409677824000, 1449104819355648000, 1449104819355648000, 1963303303643136000, 2227122185070182400, 4454244370140364800, 4873019481862963200, 5834363461278105600, 8751545191917158400, 9439403384084889600, 10619328807095500800, 21238657614191001600, 25148261254614220800, 50296522509228441600, 54129278903648256000, 73233730281406464000, 109850595422109696000, 128396799844024320000, 132118446216314880000, 163071910758422937600, 244607866137634406400, 269622877555261440000, 337028596944076800000, 674057193888153600000, 721386827100979200000, 1442773654201958400000, 1623120360977203200000, 1852877124403200000000, 2055458356671283200000, 2531459239268843520000, 2778979698219574886400, 5557959396439149772800, 8336939094658724659200, 11262180882258277171200, 11550954751034130432000, 13708825418809737216000, 14420972193812840448000, 28841944387625680896000, 36052430484532101120000, 39748082791530627072000, 59622124187295940608000, 119244248374591881216000, 125168759359779373056000, 144425491568976199680000, 162742870987480498176000, 185182651056704716800000, 231478313820880896000000, 462956627641761792000000, 546470372235961958400000, 592938941303645798400000, 627817702556801433600000, 846823877867313561600000, 1270235816800970342400000, 2540471633601940684800000, 2657938582177579008000000, 5315877164355158016000000, 5865795491702243328000000, 7908937741621002240000000, 8897554959323627520000000, 10914334083436983091200000, 12874871872498811535360000, 14825610034998631464960000, 18532012543748289331200000, 19781056612630957916160000, 22232187540717837484032000, 44464375081435674968064000, 44937400348259458744320000, 89874800696518917488640000, 134812201044778376232960000, 147825428066122044801024000, 157362552457484757368832000, 314725104914969514737664000, 338191450456875136450560000, 676382900913750272901120000, 704565521785156534272000000, 949006621180006760448000000, 1423509931770010140672000000, 1676167538707544408064000000, 1834190067609265766400000000, 2245048642753741298073600000, 3367572964130611947110400000, 3816582692681360206725120000, 4041087556956734336532480000, 4628882110695895694573568000, 4906089515746503646248960000, 9812179031493007292497920000, 12265223789366259115622400000, 16512404842641954019737600000, 24768607263962931029606400000, 30293911961308507951595520000, 31167774806346253373276160000, 36638037323378452944912384000, 54957055985067679417368576000, 73960897774296690057019392000, 78944785764478407715848192000, 89740653903210497659895808000, 105666850197761743386574848000, 211333700395523486773149696000, 217204080962065805850181632000, 229381679792762665505390592000]

200816

PARI


PARI と OneDrive

\r ○○.gp でファイルを読み込むとき、

ファイルがOneDrive 上にあると読み込めないことに

気づいた。

Windows 10 だと、特に設定し直さないかぎりデスクトップも

OneDrive の下のフォルダになっていることが多いので注意しよう。

200811

Vue.js

select

<select v-model="プロパティ名" multiple>

の複数選択について、

Ctrl を押しながら項目を選ぶというのは不便だと思う。

200808

Ruby


A243631 とA336727

A307883 とA307884 と似た関係式をもつ。

# A307883とA307884
def A(k, n)
  i, a, b = 0, 1, k + 1
  ary = [1]
  while i < n
    i += 1
    a, b = b, ((k + 1) * (2 * i + 1) * b - (k - 1) ** 2 * i * a) / (i + 1)
    ary << a
  end
  ary
end

# A243631とA336727
def B(k, n)
  i, a, b = 0, 1, 1
  ary = [1]
  while i < n
    i += 1
    a, b = b, ((k + 1) * (2 * i + 1) * b - (k - 1) ** 2 * (i - 1) * a) / (i + 2)
    ary << a
  end
  ary
end

n = 10
-10.upto(10){|i| p [i, A(i, n)]}
-10.upto(10){|i| p [i, B(i, n)]}

出力結果

[-10, [1, -9, 61, -189, -2559, 59751, -727859, 5968611, -23658239, -239767209, 6676401501]]

[-9, [1, -8, 46, -80, -2330, 39952, -391796, 2396512, -1665530, -187855280, 3005297956]]

[-8, [1, -7, 33, -7, -1919, 24633, -186591, 715449, 3834369, -102211207, 1079883553]]

[-7, [1, -6, 22, 36, -1434, 13644, -73604, 71688, 3315334, -41652036, 283869972]]

[-6, [1, -5, 13, 55, -959, 6475, -20195, -84425, 1657345, -11975525, 40678573]]

[-5, [1, -4, 6, 56, -554, 2376, -804, -67344, 530406, -1852504, -3106124]]

[-4, [1, -3, 1, 45, -255, 477, 2689, -25203, 82945, 90045, -2379519]]

[-3, [1, -2, -2, 28, -74, -92, 1324, -3656, -4826, 70228, -197372]]

[-2, [1, -1, -3, 11, 1, -81, 141, 363, -1791, 479, 13597]]

[-1, [1, 0, -2, 0, 6, 0, -20, 0, 70, 0, -252]]

[0, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]

[1, [1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620, 184756]]

[2, [1, 3, 13, 63, 321, 1683, 8989, 48639, 265729, 1462563, 8097453]]

[3, [1, 4, 22, 136, 886, 5944, 40636, 281488, 1968934, 13875544, 98365972]]

[4, [1, 5, 33, 245, 1921, 15525, 127905, 1067925, 9004545, 76499525, 653808673]]

[5, [1, 6, 46, 396, 3606, 33876, 324556, 3151896, 30915046, 305543556, 3038019876]]

[6, [1, 7, 61, 595, 6145, 65527, 712909, 7863667, 87615745, 983726695, 11112210781]]

[7, [1, 8, 78, 848, 9766, 116208, 1411404, 17383584, 216294534, 2712176048, 34217133028]]

[8, [1, 9, 97, 1161, 14721, 192969, 2582881, 35066313, 481003009, 6649718409, 92497952097]]

[9, [1, 10, 118, 1540, 21286, 304300, 4443580, 65830600, 985483270, 14869654300, 225759595348]]

[10, [1, 11, 141, 1991, 29761, 460251, 7272861, 116619591, 1889815041, 30869546411, 507406003501]]

[-10, [1, 1, -9, 71, -459, 1901, 4851, -214709, 2829321, -25102759, 141253551]]

[-9, [1, 1, -8, 55, -296, 802, 6832, -138941, 1397080, -9274418, 26549776]]

[-8, [1, 1, -7, 41, -175, 177, 6153, -78951, 588833, -2530591, -4090471]]

[-7, [1, 1, -6, 29, -90, -118, 4404, -38219, 194286, -269506, -6250068]]

[-6, [1, 1, -5, 19, -35, -203, 2575, -14705, 38425, 177769, -2904605]]

[-5, [1, 1, -4, 11, -4, -174, 1176, -3729, -3364, 116846, -719224]]

[-4, [1, 1, -3, 5, 9, -103, 357, -131, -5295, 29297, -55539]]

[-3, [1, 1, -2, 1, 10, -38, 28, 289, -1262, 1054, 11044]]

[-2, [1, 1, -1, -1, 5, -3, -21, 51, 41, -391, 407]]

[-1, [1, 1, 0, -1, 0, 2, 0, -5, 0, 14, 0]]

[0, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]

[1, [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796]]

[2, [1, 1, 3, 11, 45, 197, 903, 4279, 20793, 103049, 518859]]

[3, [1, 1, 4, 19, 100, 562, 3304, 20071, 124996, 793774, 5120632]]

[4, [1, 1, 5, 29, 185, 1257, 8925, 65445, 491825, 3768209, 29324405]]

[5, [1, 1, 6, 41, 306, 2426, 20076, 171481, 1500666, 13386206, 121267476]]

[6, [1, 1, 7, 55, 469, 4237, 39907, 387739, 3858505, 39130777, 402972031]]

[7, [1, 1, 8, 71, 680, 6882, 72528, 788019, 8766248, 99362894, 1143498224]]

[8, [1, 1, 9, 89, 945, 10577, 123129, 1476841, 18130401, 226739489, 2878666857]]

[9, [1, 1, 10, 109, 1270, 15562, 198100, 2596645, 34825150, 475697854, 6595646860]]

[10, [1, 1, 11, 131, 1661, 22101, 305151, 4335711, 63009881, 932449961, 14004694451]]