A305407 -id:A305407 - cp's OEIS frontend

A353994 Expansion of e.g.f. 1/(1 + log(1 - x) * (exp(x) - 1)).

1, 0, 2, 6, 42, 305, 2815, 29792, 362432, 4952481, 75239143, 1257202584, 22918653428, 452620972245, 9626556838015, 219367419292972, 5332164894151648, 137709755844024929, 3765736630207259055, 108696751776637007080, 3302628833563666988740

Offset: 0

Seiichi Manyama, May 13 2022

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..421

Cf. A052830, A052848, A052863, A305407, A353995.

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

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

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

Original entry on oeis.org

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

Seiichi Manyama, May 04 2022

nonn

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

Cf. A002741, A298374, A305407.

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 *)

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

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

cp's OEIS Frontend

A353994 Expansion of e.g.f. 1/(1 + log(1 - x) * (exp(x) - 1)).

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