A371198 Expansion of e.g.f. 1/(1 + x^3 * log(1 - x - x^2)).

1, 0, 0, 0, 24, 180, 960, 8820, 129024, 2177280, 32875200, 533887200, 9997827840, 212133841920, 4799669696640, 114208231737600, 2901190960926720, 79007705121945600, 2289453730357248000, 69972073047194572800, 2249392810263651532800

Offset: 0

Author

Seiichi Manyama, Mar 15 2024

Keywords

• nonn

Crossrefs

Cf. A371196, A371197.

Cf. A371158.

Programs

PARI

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

Formula

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