A367881
Expansion of e.g.f. 1/(1 - 3 * x * (exp(x) - 1)).
Original entry on oeis.org
1, 0, 6, 9, 228, 1095, 23238, 215481, 4657992, 66216555, 1553967210, 29793656013, 777115661292, 18608934688383, 542832959656302, 15470567460571905, 503794462155308688, 16557037363336856019, 598704921471691072242, 22205328374455141122165
Offset: 0
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a(n) = n!*sum(k=0, n\2, 3^k*k!*stirling(n-k, k, 2)/(n-k)!);
A375683
Expansion of e.g.f. 1 / (1 + x * (exp(x) - 1)).
Original entry on oeis.org
1, 0, -2, -3, 20, 115, -306, -6307, -6616, 462663, 2956130, -38945951, -656504388, 2325876683, 145820995670, 562691968005, -33452317341616, -449954883966065, 7055017491780810, 233802046526955497, -571834988279277340, -112474674691684827501
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*(exp(x)-1))))
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a(n) = n!*sum(k=0, n\2, (-1)^k*k!*stirling(n-k, k, 2)/(n-k)!);
A375695
Expansion of e.g.f. 1 / sqrt(1 - 2 * x * (exp(x) - 1)).
Original entry on oeis.org
1, 0, 2, 3, 40, 185, 2436, 20797, 307616, 3869217, 66259900, 1091351261, 21671302368, 437191547377, 9981020325836, 236821065758565, 6144729994822336, 167019469703969345, 4868403452056231164, 148845363155530699789, 4822574537456548631360
Offset: 0
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With[{nn=20},CoefficientList[Series[1/Sqrt[1-2x (Exp[x]-1)],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Feb 06 2025 *)
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1-2*x*(exp(x)-1))))
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a001147(n) = prod(k=0, n-1, 2*k+1);
a(n) = n!*sum(k=0, n, a001147(k)*stirling(n-k, k, 2)/(n-k)!);
Showing 1-3 of 3 results.