A305988 Expansion of e.g.f. 1/(1 + log(2 - exp(x))).

1, 1, 4, 24, 194, 1970, 24062, 343294, 5601122, 102847794, 2098766582, 47117285270, 1154031484586, 30622256174458, 875092190716382, 26794239236959806, 875110094707912562, 30367988674208286914, 1115822099409002188358, 43276913813553367194598, 1766830322476935945014330

Offset: 0

Author

Ilya Gutkovskiy, Jun 15 2018

Keywords

• nonn

Comments

Stirling transform of A007840.

Examples

			1/(1 + log(2 - exp(x))) = 1 + x + 4*x^2/2! + 24*x^3/3! + 194*x^4/4! + 1970*x^5/5! + 24062*x^6/6! + ...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..402
• N. J. A. Sloane, Transforms
• Eric Weisstein's World of Mathematics, Stirling Transform

Crossrefs

Cf. A000629, A000670, A007840, A050351, A083355, A305323.

Programs

Maple

b:= proc(n) b(n):= n!*`if`(n=0, 1, add(b(k)/(k!*(n-k)), k=0..n-1)) end:
a:= n-> add(Stirling2(n, j)*b(j$2), j=0..n):
seq(a(n), n=0..25);  # Alois P. Heinz, Jun 15 2018

Mathematica

nmax = 20; CoefficientList[Series[1/(1 + Log[2 - Exp[x]]), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Sum[StirlingS2[n, k] Abs[StirlingS1[k, j]] j!, {j, 0, k}], {k, 0, n}], {n, 0, 20}]

Formula

a(n) = Sum_{k=0..n} Stirling2(n,k)*A007840(k).

a(n) ~ n! / ((2*exp(1) - 1) * (log(2 - exp(-1)))^(n+1)). - Vaclav Kotesovec, Jul 01 2018