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

0,3

Links

Table of n, a(n) for n=0..16.

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

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 *)

Prog

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

Crossrefs

Cf. A007840, A052802, A367138.

Cf. A367135, A367137.

Sequence in context: A180831 A361094 A367135 * A180819 A132874 A223289

Adjacent sequences: A367136 A367137 A367138 * A367140 A367141 A367142

Keyword

nonn

Author

Seiichi Manyama, Nov 06 2023

Status

approved