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

0,3

Links

Table of n, a(n) for n=0..18.

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)! ).

Prog

(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)!));

Crossrefs

Cf. A161631, A364978.

Sequence in context: A163068 A109684 A292134 * A137287 A155872 A323478

Adjacent sequences: A364976 A364977 A364978 * A364980 A364981 A364982

Keyword

nonn

Author

Seiichi Manyama, Aug 15 2023

Status

approved