A379942 Expansion of e.g.f. 1/( exp(-x) - x )^3.

1, 6, 45, 411, 4449, 55803, 796581, 12757503, 226588257, 4420898595, 94001021589, 2163619250895, 53598352999905, 1421924243354787, 40221778417553637, 1208471542554184767, 38434396264371831873, 1289995362325669726659, 45567027291743788320405

Offset: 0

Author

Seiichi Manyama, Jan 07 2025

Keywords

• nonn

Crossrefs

Cf. A072597, A379933, A379943.

Cf. A377530.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(exp(-x)-x)^3))

PARI

a(n) = n!*sum(k=0, n, (k+3)^(n-k)*binomial(k+2, 2)/(n-k)!);

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A072597.

a(n) = n! * Sum_{k=0..n} (k+3)^(n-k) * binomial(k+2,2)/(n-k)!.