A362912 Expansion of e.g.f. 1/( 1 - (exp(x) - 1) * exp(exp(x) - 1) ).

1, 1, 5, 34, 303, 3371, 45016, 701401, 12490057, 250215916, 5569582777, 136371309999, 3642603629462, 105405416033607, 3284722016179597, 109672448519030698, 3905936524326557659, 147802493781420536423, 5921911678533323178312

Offset: 0

Author

Seiichi Manyama, May 10 2023

Keywords

• nonn

Crossrefs

Cf. A305306, A362911.

Cf. A006153, A347339.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-(exp(x)-1)*exp(exp(x)-1))))

Formula

a(n) = Sum_{k=0..n} Stirling2(n,k) * A006153(k).

a(n) ~ n! * LambertW(1) / ((1 + LambertW(1))^2 * (log(1 + LambertW(1)))^(n+1)). - Vaclav Kotesovec, Nov 11 2023