A365030 E.g.f. satisfies A(x) = exp(x * (1 + x * A(x))^3).

1, 1, 7, 55, 709, 11761, 243181, 6054763, 175803097, 5847578785, 219175994521, 9144024668131, 420340277237365, 21111584238219697, 1150333949592549541, 67589878866533749531, 4260172601206280708401, 286737199114729515029569

Offset: 0

Author

Seiichi Manyama, Aug 17 2023

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..363

Crossrefs

Cf. A125500, A363744.

Cf. A364938.

Programs

Mathematica

Array[#!*Sum[ (# - k + 1)^(k - 1)*Binomial[3 k, # - k]/k!, {k, 0, #}] &, 18, 0] (* Michael De Vlieger, Aug 18 2023 *)

PARI

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

Formula

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