A353995 Expansion of e.g.f. 1/(1 - x)^(exp(x) - 1).

1, 0, 2, 6, 30, 185, 1315, 10682, 97692, 991797, 11060413, 134368344, 1766007122, 24963786003, 377633418279, 6086719267852, 104134471945368, 1884698592318537, 35976835400864745, 722386383476096128, 15220456179011671358, 335769403850849998439

Offset: 0

Author

Seiichi Manyama, May 13 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..449

Crossrefs

Cf. A052863, A191365, A353994.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[1/(1-x)^(Exp[x]-1),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Aug 03 2025 *)

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x)^(exp(x)-1)))

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-log(1-x)*(exp(x)-1))))

Formula

E.g.f.: exp( -log(1 - x) * (exp(x) - 1) ).

a(0) = 1; a(n) = Sum_{k=1..n} A052863(k) * binomial(n-1,k-1) * a(n-k).

a(n) ~ n! * n^(exp(1)-2) / Gamma(exp(1)-1) * (1 - (exp(1)-2)*exp(1)*log(n)/n). - Vaclav Kotesovec, May 13 2022