A375681 Expansion of e.g.f. 1 / (1 + x * log(1 - x^2))^3.

1, 0, 0, 18, 0, 180, 4320, 5040, 241920, 3900960, 19958400, 622702080, 9580032000, 112086374400, 3013462932480, 52540488000000, 977094287769600, 25683596370432000, 540291743902310400, 13061642656398336000, 360218657273739264000, 9111103133582241792000

Offset: 0

Author

Seiichi Manyama, Aug 23 2024

Keywords

• nonn

Crossrefs

Cf. A375561, A375680.

Cf. A375665.

Programs

PARI

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

PARI

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

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A375561.

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