A375628 Expansion of e.g.f. exp(2*x^3) / (1 - x * exp(x^3)).

1, 1, 2, 18, 96, 600, 5760, 57960, 645120, 8285760, 117936000, 1842825600, 31374604800, 578334556800, 11493004723200, 244720360684800, 5555523785011200, 134002274473267200, 3422904611167641600, 92290617116425728000, 2619214995575033856000

Offset: 0

Author

Seiichi Manyama, Aug 21 2024

Keywords

• nonn

Crossrefs

Cf. A368265, A375627.

Cf. A358065, A375607.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x^3)/(1-x*exp(x^3))))

PARI

a(n) = n!*sum(k=0, n\3, (n-3*k+2)^k/k!);

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k+2)^k/k!.