A375679 Expansion of e.g.f. 1 / (1 + x^2 * log(1 - x))^3.

1, 0, 0, 18, 36, 120, 4860, 33264, 241920, 5598720, 72364320, 879500160, 18172978560, 331463508480, 5726430597888, 126134466796800, 2836325702246400, 62773403361177600, 1562890149787392000, 41009994647421972480, 1090182759179092992000

Offset: 0

Author

Seiichi Manyama, Aug 23 2024

Keywords

• nonn

Crossrefs

Cf. A351503, A375639.

Cf. A375663.

Programs

PARI

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

PARI

a(n) = n!*sum(k=0, n\3, (k+2)!*abs(stirling(n-2*k, k, 1))/(n-2*k)!)/2;

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A351503.

a(n) = (n!/2) * Sum_{k=0..floor(n/3)} (k+2)! * |Stirling1(n-2*k,k)|/(n-2*k)!.