A292889 Expansion of e.g.f. exp(x^3 * exp(x)).

1, 0, 0, 6, 24, 60, 480, 5250, 40656, 302904, 3024720, 35260830, 400499880, 4619610996, 58758862344, 813678468330, 11686918766880, 173172973038960, 2695921067029536, 44219170187746614, 755363769931590840, 13351503268881437100, 244634794020399856920

Offset: 0

Author

Seiichi Manyama, Sep 26 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..498

Crossrefs

Column k=3 of A292978.

Cf. A145453, A292891, A292908.

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