A375699 Expansion of e.g.f. 1 / (1 + x^3 * log(1 - x))^(1/6).

1, 0, 0, 0, 4, 10, 40, 210, 5264, 45360, 409800, 4065600, 77948640, 1183422240, 17527233360, 267109642800, 5422495921920, 110998923235200, 2270809072896000, 47142009514454400, 1116394268619772800, 27963045712157472000, 718066383283082803200

Offset: 0

Author

Seiichi Manyama, Aug 25 2024

Keywords

• nonn

Crossrefs

Cf. A351504, A375700, A375701.

Cf. A008542, A351506.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x^3*log(1-x))^(1/6)))

PARI

a(n) = n!*sum(k=0, n\4, prod(j=0, k-1, 6*j+1)*abs(stirling(n-3*k, k, 1))/(6^k*(n-3*k)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} (Product_{j=0..k-1} (6*j+1)) * |Stirling1(n-3*k,k)|/(6^k*(n-3k)!).