A375663 Expansion of e.g.f. 1 / (1 - x^2 * (exp(x) - 1))^3.

1, 0, 0, 18, 36, 60, 4410, 30366, 141288, 4173336, 56307150, 504947850, 10795641516, 209176625268, 2958760573314, 60807476490390, 1419440085948240, 27655117897680816, 621153635750802198, 16250306025184563330, 396542042830732066260, 10152940698142734694860

Offset: 0

Author

Seiichi Manyama, Aug 23 2024

Keywords

• nonn

Crossrefs

Cf. A358013, A375662.

Programs

PARI

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

PARI

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

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A358013.

a(n) = (n!/2) * Sum_{k=0..floor(n/3)} (k+2)! * Stirling2(n-2*k,k)/(n-2*k)!.