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
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..449
Programs
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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