A292979 Expansion of e.g.f. exp(x^4 * exp(x)).

1, 0, 0, 0, 24, 120, 360, 840, 21840, 365904, 3633840, 26619120, 239512680, 3943797000, 69258333144, 997361197560, 12707273822880, 179576670930720, 3215428464641760, 62865157116396384, 1167555972633639480, 20756362432008412440, 386561667091927394760

Offset: 0

Author

Seiichi Manyama, Sep 27 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..487

Crossrefs

Column k=4 of A292978.

Cf. A292969.

Programs

PARI

x='x+O('x^66); Vec(serlaplace(exp(x^4*exp(x))))

PARI

a(n) = n!*sum(k=0, n\4, k^(n-4*k)/(k!*(n-4*k)!)); \\ Seiichi Manyama, Jul 10 2022

Formula

a(n) = (-1)^n * A292969(n).

a(n) = n! * Sum_{k=0..floor(n/4)} k^(n-4*k)/(k! * (n-4*k)!). - Seiichi Manyama, Jul 10 2022