A375680 Expansion of e.g.f. 1 / (1 + x * log(1 - x^2))^2.

1, 0, 0, 12, 0, 120, 2160, 3360, 120960, 1632960, 9979200, 255467520, 3592512000, 45664819200, 1070840010240, 18027225216000, 340344048844800, 8174882722406400, 169308486085939200, 4019018956285132800, 104511967278630912000, 2606273308503760896000

Offset: 0

Author

Seiichi Manyama, Aug 23 2024

Keywords

• nonn

Crossrefs

Cf. A375561, A375681.

Cf. A375664.

Programs

PARI

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

PARI

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A375561.

a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1)! * |Stirling1(k,n-2*k)|/k!.