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

0,5

Links

Table of n, a(n) for n=0..22.

Formula

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

Prog

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

Crossrefs

Column k=3 of A154602.

Sequence in context: A181277 A181269 A004333 * A016237 A036735 A321456

Adjacent sequences: A383202 A383203 A383204 * A383206 A383207 A383208

Keyword

nonn

Author

Seiichi Manyama, Apr 19 2025

Status

approved