A375664 Expansion of e.g.f. 1 / (1 - x * (exp(x^2) - 1))^2.

1, 0, 0, 12, 0, 120, 2160, 1680, 120960, 1481760, 6350400, 240166080, 2754259200, 31152401280, 894303970560, 11769588230400, 228232766361600, 5845147711603200, 98290727395660800, 2502848611354291200, 63417766359467520000, 1376904298716724377600

Offset: 0

Author

Seiichi Manyama, Aug 23 2024

Keywords

• nonn

Crossrefs

Cf. A375588, A375665.

Programs

PARI

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

PARI

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A375588.

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