A364986 E.g.f. satisfies A(x) = 1 + x*A(x)^3*exp(x*A(x)^3).

1, 1, 8, 129, 3196, 107465, 4575966, 236120059, 14322901832, 998966928897, 78770826493210, 6929685905371691, 672900446143476156, 71491442785783506577, 8249400210035835040022, 1027394346436911560475915, 137360293432089585554830096

Offset: 0

Author

Seiichi Manyama, Aug 15 2023

Keywords

• nonn

Crossrefs

Cf. A364983, A364984, A364985.

Cf. A161633, A364982, A364989.

Cf. A002293.

Programs

PARI

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

Formula

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