A379943 Expansion of e.g.f. 1/( exp(-x) - x )^4.

1, 8, 76, 844, 10776, 155844, 2520856, 45125924, 886037216, 18938440324, 437820992136, 10886467502244, 289738784758096, 8218731027307844, 247539834718198136, 7889896358130120484, 265325716114102815936, 9388476560982511842564, 348703400008471862936296

Offset

0,2

Links

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

Formula

E.g.f.: B(x)^4, where B(x) is the e.g.f. of A072597.

a(n) = n! * Sum_{k=0..n} (k+4)^(n-k) * binomial(k+3,3)/(n-k)!.

a(n) ~ sqrt(Pi/2) * n^(n + 7/2) / (3 * (1 + LambertW(1))^4 * LambertW(1)^(n+4) * exp(n)). - Vaclav Kotesovec, Feb 04 2026

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(exp(-x)-x)^4))
(PARI) a(n) = n!*sum(k=0, n, (k+4)^(n-k)*binomial(k+3, 3)/(n-k)!);

Crossrefs

Cf. A072597, A379933, A379942.

Sequence in context: A383884 A233827 A231286 * A251927 A024281 A232087

Adjacent sequences: A379940 A379941 A379942 * A379944 A379945 A379946

Keyword

nonn

Author

Seiichi Manyama, Jan 07 2025

Status

approved