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

0,2

Links

Table of n, a(n) for n=0..18.

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)!.

a(n) ~ sqrt(Pi/2) * n^(n + 5/2) / ((1 + LambertW(1))^3 * LambertW(1)^(n+3) * exp(n)). - Vaclav Kotesovec, Feb 04 2026

Prog

(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)!);

Crossrefs

Cf. A072597, A379933, A379943.

Cf. A377530.

Sequence in context: A135148 A137974 A371541 * A291421 A001879 A019577

Adjacent sequences: A379939 A379940 A379941 * A379943 A379944 A379945

Keyword

nonn

Author

Seiichi Manyama, Jan 07 2025

Status

approved