A383204 Expansion of e.g.f. f(x)^2 * exp(f(x)) / 2, where f(x) = (exp(2*x) - 1)/2.

0, 0, 1, 9, 70, 550, 4531, 39515, 365324, 3575820, 36971461, 402741581, 4610187154, 55316069874, 694067320311, 9087012399007, 123889735839000, 1755654433460248, 25816120675972105, 393285627390135313, 6198118449550830302, 100916786871955767998, 1695424878199285059003

Offset: 0

Author

Seiichi Manyama, Apr 19 2025

Keywords

• nonn

Crossrefs

Column k=2 of A154602.

Programs

PARI

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

Formula

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