A375796 Expansion of e.g.f. 1/(1 - (exp(x^3) - 1)/x^2).

1, 1, 2, 6, 36, 240, 1800, 15960, 164640, 1905120, 24343200, 342619200, 5269017600, 87749101440, 1573083832320, 30218175187200, 619256461824000, 13483023576422400, 310821905134540800, 7563477205380096000, 193736838233562624000, 5210638309494858240000

Offset: 0

Author

Seiichi Manyama, Aug 29 2024

Keywords

• nonn

Crossrefs

Cf. A000670, A375795.

Cf. A357964.

Programs

PARI

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

PARI

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

Formula

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