A375634 Expansion of e.g.f. exp(x^3) / (1 - x * exp(x^3/6)).

1, 1, 2, 12, 52, 280, 2160, 16870, 150080, 1557360, 17491600, 215908000, 2923905600, 42734091400, 672515043200, 11347480544400, 204142655516800, 3902009862150400, 78976503077472000, 1687212801048174400, 37941749192547200000

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} ((n-3*k+6)/6)^k/k!.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^3)/(1-x*exp(x^3/6))))
(PARI) a(n) = n!*sum(k=0, n\3, ((n-3*k+6)/6)^k/k!);

Crossrefs

Cf. A358265, A375607, A375633.

Sequence in context: A080675 A218782 A007225 * A139046 A036359 A055703

Adjacent sequences: A375631 A375632 A375633 * A375635 A375636 A375637

Keyword

nonn

Author

Seiichi Manyama, Aug 22 2024

Status

approved