A383196 Expansion of e.g.f. (1/(1 - 3*x)^(1/3) - 1)^3 / 6.

0, 0, 0, 1, 24, 520, 11880, 295960, 8090880, 242280640, 7912262400, 280384720000, 10727852889600, 441104638374400, 19407654326860800, 910140650683264000, 45332366929833984000, 2390437704451084288000, 133060566042200788992000, 7797805996570952986624000

Offset: 0

Author

Seiichi Manyama, Apr 19 2025

Keywords

• nonn

Crossrefs

Column k=3 of A371080.

Cf. A001754, A035119, A143169.

Programs

PARI

a(n) = sum(k=3, n, 3^(n-k)*abs(stirling(n, k, 1))*stirling(k, 3, 2));

Formula

a(n) = Sum_{k=3..n} 3^(n-k) * |Stirling1(n,k)| * Stirling2(k,3).

a(n) ~ sqrt(Pi/2) * n^(n + 1/2) * 3^(n-1) * exp(-n) * (1 - 3/(Gamma(2/3)*n^(1/3))). - Vaclav Kotesovec, May 03 2025