A316747
Stirling transform of (2*n)!.
Original entry on oeis.org
1, 2, 26, 794, 44810, 4050362, 536119946, 97759687034, 23495075990090, 7197163489723322, 2737224615568742666, 1265459307754418362874, 698926543187678223962570, 454516898016585094157146682, 343753040265700944173260034186, 299168865461564926143049346952314
Offset: 0
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Table[Sum[StirlingS2[n, k]*(2*k)!, {k, 0, n}], {n, 0, 20}]
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (2*k)!*(exp(x)-1)^k/k!))) \\ Seiichi Manyama, May 20 2022
A308491
a(0) = 1, a(n) = Sum_{k=1..n} stirling2(n,k) * k^(3*k).
Original entry on oeis.org
1, 1, 65, 19876, 16895763, 30685843321, 102018812632786, 560682901512212459, 4738032814084465062121, 58320000513552476843995786, 1002620283226568243192938115197, 23280221638971518379191182864465213, 710336441472841166799952152725333251616
Offset: 0
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Join[{1}, Table[Sum[k^(3*k)*StirlingS2[n, k], {k, 1, n}], {n, 1, 15}]]
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^3*(exp(x)-1))^k/k!))) \\ Seiichi Manyama, Feb 04 2022
A354250
Expansion of e.g.f. Sum_{k>=0} (3*k)! * log(1+x)^k / k!.
Original entry on oeis.org
1, 6, 714, 360732, 476832204, 1302897016944, 6382799223892560, 50956720815425427360, 619019914356960664044960, 10866561174598537960652828160, 264763399994627082733034386813440, 8668743073576807048450006051943930880
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (3*k)!*log(1+x)^k/k!)))
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a(n) = sum(k=0, n, (3*k)!*stirling(n, k, 1));
A354251
Expansion of e.g.f. Sum_{k>=0} (3*k)! * (-log(1-x))^k / k!.
Original entry on oeis.org
1, 6, 726, 365052, 481186836, 1312477120944, 6422029618230000, 51225621215200895520, 621881012244669445985760, 10911233517605729917096273920, 265743399210784245852461349120000, 8697920910678436598411074217669652480
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (3*k)!*(-log(1-x))^k/k!)))
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a(n) = sum(k=0, n, (3*k)!*abs(stirling(n, k, 1)));
Showing 1-4 of 4 results.