A367139 E.g.f. satisfies A(x) = 1/(1 + log(1 - x*A(x)^3)).

1, 1, 9, 167, 4780, 186004, 9173780, 548563140, 38573633016, 3119384230176, 285237426927552, 29102185296785160, 3277703460197645232, 403931173342682581296, 54066960915411480743520, 7811249803193620134996864, 1211525560869437165319590400

Offset: 0

Author

Seiichi Manyama, Nov 06 2023

Keywords

• nonn

Crossrefs

Cf. A007840, A052802, A367138.

Cf. A367135, A367137.

Programs

Mathematica

Table[1/(3*n+1)! * Sum[(3*n+k)! * Abs[StirlingS1[n,k]], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 07 2023 *)

PARI

a(n) = sum(k=0, n, (3*n+k)!*abs(stirling(n, k, 1)))/(3*n+1)!;

Formula

a(n) = (1/(3*n+1)!) * Sum_{k=0..n} (3*n+k)! * |Stirling1(n,k)|.

a(n) ~ LambertW(3*exp(4))^n * n^(n-1) / (sqrt(3*(1 + LambertW(3*exp(4)))) * exp(n) * (-3 + LambertW(3*exp(4)))^(4*n + 1)). - Vaclav Kotesovec, Nov 07 2023