A383205 Expansion of e.g.f. f(x)^3 * exp(f(x)) / 6, where f(x) = (exp(2*x) - 1)/2.

0, 0, 0, 1, 16, 190, 2080, 22491, 247072, 2792476, 32659840, 396255541, 4991365808, 65268062938, 885442472096, 12451577262671, 181326192307264, 2731564737248696, 42522062246582784, 683301050932028777, 11322975536640636240, 193300021823406703990, 3396381539718451143200

Offset: 0

Author

Seiichi Manyama, Apr 19 2025

Keywords

• nonn

Crossrefs

Column k=3 of A154602.

Programs

PARI

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

Formula

a(n) = Sum_{k=3..n} 2^(n-k) * binomial(k,3) * Stirling2(n,k).