A363479 E.g.f. satisfies A(x) = exp(x * A(x)^3 * (1 + x * A(x)^3)).

1, 1, 9, 160, 4381, 162816, 7663669, 437164288, 29317265625, 2260685099008, 197088986941921, 19170218777296896, 2058199476739788661, 241779221463040000000, 30847476924400409437389, 4247859315849037948911616, 627960846411135123552180529

Offset: 0

Author

Seiichi Manyama, Aug 17 2023

Keywords

• nonn

Crossrefs

Cf. A088695, A363358.

Cf. A361094.

Programs

PARI

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

Formula

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