A375811 Expansion of e.g.f. 1/(1 - (exp(x^2) - 1)/x)^3.

1, 3, 12, 69, 504, 4380, 44280, 509670, 6572160, 93813552, 1467910080, 24976440720, 459045195840, 9061616266560, 191187467190720, 4293103436622000, 102216550583347200, 2572022267758944000, 68195046359419499520, 1900236334204732043520

Offset: 0

Author

Seiichi Manyama, Aug 29 2024

Keywords

• nonn

Crossrefs

Cf. A375795, A375810.

Cf. A375665.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-(exp(x^2)-1)/x)^3))

PARI

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

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A375795.

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