A292969 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

Offset: 0

Author

Seiichi Manyama, Sep 27 2017

Keywords

• sign

Links

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

Crossrefs

Column k=4 of A292973.

Cf. A292979.

Programs

Maple

S:= series(exp(x^4*exp(-x)),x,51):
seq(coeff(S,x,j)*j!,j=0..50); # Robert Israel, Sep 28 2017

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