A377578 E.g.f. satisfies A(x) = (1 + x * exp(x*A(x)))^3.

1, 3, 12, 105, 1308, 21375, 441018, 10896123, 315264792, 10449447579, 390569672910, 16257117737223, 745842771924660, 37396841181068343, 2034701509480503906, 119398947940954110915, 7517149983020119420848, 505442237612562154098099, 36150074712773275030075926

Offset: 0

Author

Seiichi Manyama, Nov 02 2024

Keywords

• nonn

Crossrefs

Cf. A161632, A377579.

Cf. A364979.

Programs

PARI

a(n) = n!*sum(k=0, n, k^(n-k)*binomial(3*n-3*k+3, k)/((n-k+1)*(n-k)!));

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A364979.

a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(3*n-3*k+3,k)/( (n-k+1)*(n-k)! ).