A351739 Expansion of e.g.f. 1/(1 + log(1-x))^x.

1, 0, 2, 6, 40, 295, 2688, 28588, 348864, 4802922, 73652110, 1245046836, 23003289912, 461188427544, 9972307487660, 231341792369010, 5731422576446208, 151032969213699536, 4218265874407103640, 124471244064061267032, 3869361472890037713560

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A052809(k) * binomial(n-1,k-1) * a(n-k).

a(n) ~ n! * exp(n) / (Gamma(1 - 1/exp(1)) * n^(1/exp(1)) * (exp(1) - 1)^(n + 1 - 1/exp(1))). - Vaclav Kotesovec, Jun 04 2022

Prog

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

Crossrefs

Cf. A052801, A052809, A354122, A354123.

Sequence in context: A333631 A337071 A354313 * A098854 A056787 A098852

Adjacent sequences: A351736 A351737 A351738 * A351740 A351741 A351742

Keyword

nonn

Author

Seiichi Manyama, May 20 2022

Status

approved