A375807 Expansion of e.g.f. 1/(1 + (log(1 - x^2))/x)^3.

1, 3, 12, 69, 504, 4440, 45720, 538020, 7116480, 104455008, 1684005120, 29571696000, 561695238720, 11472451848000, 250694772007680, 5835284153899200, 144124039400140800, 3764378233282867200, 103661897106414366720, 3001493647870874956800

Offset: 0

Author

Seiichi Manyama, Aug 29 2024

Keywords

• nonn

Crossrefs

Cf. A375798, A375806.

Cf. A375681.

Programs

PARI

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

PARI

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

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A375798.

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