A364979 E.g.f. satisfies A(x) = 1 + x*exp(x*A(x)^3).

1, 1, 2, 21, 220, 3545, 70566, 1702267, 48438104, 1582227873, 58475787850, 2410935939731, 109728296017572, 5464423604085745, 295562179335075758, 17255009243888243115, 1081438061864539992496, 72422934220506772042817, 5161269584065131270532242

Offset: 0

Author

Seiichi Manyama, Aug 15 2023

Keywords

• nonn

Crossrefs

Cf. A161631, A364978.

Programs

PARI

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

Formula

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