A375812 Expansion of e.g.f. 1/(1 - (exp(x^3) - 1)/x^2)^2.

1, 2, 6, 24, 144, 1080, 9360, 92400, 1038240, 13063680, 181137600, 2744280000, 45145900800, 801313793280, 15256927445760, 310158565516800, 6705376386508800, 153609543947059200, 3716764672074854400, 94715288771578675200, 2535525218048030208000

Offset: 0

Author

Seiichi Manyama, Aug 29 2024

Keywords

• nonn

Crossrefs

Cf. A375796, A375813.

Programs

PARI

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

PARI

a(n) = n!*sum(k=0, n\3, (n-3*k+1)!*stirling(n-2*k, n-3*k, 2)/(n-2*k)!);

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A375796.

a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k+1)! * Stirling2(n-2*k,n-3*k)/(n-2*k)!.