A354122 Expansion of e.g.f. 1/(1 + log(1 - x))^3.

1, 3, 15, 102, 870, 8892, 105708, 1431168, 21722136, 365105928, 6729341832, 134915992560, 2922576142320, 68013701197920, 1692075061072800, 44810389419079680, 1258472984174461440, 37357062009383877120, 1168635883239630120960, 38424619272539153157120

Offset: 0

Author

Seiichi Manyama, May 17 2022

Keywords

• nonn

Crossrefs

Cf. A007840, A052801, A354123.

Cf. A226515, A354120.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x))^3))

PARI

a(n) = sum(k=0, n, (k+2)!*abs(stirling(n, k, 1)))/2;

Formula

a(n) = (1/2) * Sum_{k=0..n} (k + 2)! * |Stirling1(n,k)|.

a(n) ~ sqrt(Pi/2) * n^(n + 5/2) / (exp(1) - 1)^(n+3). - Vaclav Kotesovec, Jun 04 2022

a(0) = 1; a(n) = Sum_{k=1..n} (2*k/n + 1) * (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, Nov 19 2023