A292908 Expansion of e.g.f. exp(x^3 * exp(-x)).

1, 0, 0, 6, -24, 60, 240, -4830, 39984, -180936, -605520, 24616350, -318005160, 2385790836, -86488584, -350543790870, 6917020827360, -79778558317200, 357117438258144, 9237998478286134, -304182278908538040, 5166739059890655660, -48968796671246843160

Offset: 0

Author

Seiichi Manyama, Sep 26 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..505

Crossrefs

Column k=3 of A292973.

Cf. A292889.

Programs

PARI

x='x+O('x^66); Vec(serlaplace(exp(x^3*exp(-x))))

PARI

a(n) = n!*sum(k=0, n\3, (-k)^(n-3*k)/(k!*(n-3*k)!)); \\ Seiichi Manyama, Jul 10 2022

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (-k)^(n-3*k)/(k! * (n-3*k)!). - Seiichi Manyama, Jul 10 2022