A351502 Expansion of e.g.f. 1/(1 + log(1 - x)*exp(-x)).

1, 1, 1, 2, 10, 59, 373, 2736, 23504, 229029, 2477219, 29473344, 383104588, 5401356583, 82069677701, 1336740758544, 23234632127072, 429259519490985, 8399672396793063, 173538299521211128, 3774815414843398588, 86230662745426403771, 2063931187442813081881

Offset: 0

Author

Seiichi Manyama, May 04 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..443

Crossrefs

Cf. A002741, A298374, A305407.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[1/(1+Log[1-x]Exp[-x]),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 03 2023 *)

PARI

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

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A002741(k) * binomial(n,k) * a(n-k).