A354123 Expansion of e.g.f. 1/(1 + log(1 - x))^4.

1, 4, 24, 188, 1804, 20416, 265640, 3901320, 63776280, 1147796160, 22540858080, 479500074720, 10980929163360, 269298981833280, 7040446188020160, 195439047629422080, 5740498087530831360, 177855276360034736640, 5796391124741936993280

Offset: 0

Author

Seiichi Manyama, May 17 2022

Keywords

• nonn

Crossrefs

Cf. A007840, A052801, A354122.

Cf. A226738, A354121.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x))^4))

PARI

a(n) = sum(k=0, n, (k+3)!*abs(stirling(n, k, 1)))/6;

Formula

a(n) = (1/6) * Sum_{k=0..n} (k + 3)! * |Stirling1(n,k)|.

a(n) ~ sqrt(Pi/2) * n^(n + 7/2) / (3 * (exp(1) - 1)^(n+4)). - Vaclav Kotesovec, Jun 04 2022

a(0) = 1; a(n) = Sum_{k=1..n} (3*k/n + 1) * (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, Nov 19 2023