A377530 Expansion of e.g.f. 1/(1 - x * exp(x))^3.

1, 3, 18, 141, 1380, 16095, 217458, 3335745, 57225528, 1085066523, 22526087070, 508042140573, 12367076890644, 323130848000727, 9018976230237834, 267789942962863065, 8427492557547704688, 280194087519310655667, 9813332205452943323190, 361109786425470021564021

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

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

a(n) ~ n! * n^2 / (2 * (1+LambertW(1))^3 * LambertW(1)^n). - Vaclav Kotesovec, Oct 31 2024

Mathematica

nmax=19; CoefficientList[Series[1/(1 - x * Exp[x])^3, {x, 0, nmax}], x]Range[0, nmax]! (* Stefano Spezia, Feb 05 2025 *)

Prog

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

Crossrefs

Cf. A006153, A377529.

Cf. A377532, A377534.

Cf. A377504.

Sequence in context: A186266 A260506 A193237 * A385308 A325996 A364417

Adjacent sequences: A377527 A377528 A377529 * A377531 A377532 A377533

Keyword

nonn,easy

Author

Seiichi Manyama, Oct 30 2024

Status

approved