A367135 E.g.f. satisfies A(x) = 1/(2 - exp(x*A(x)^3)).

1, 1, 9, 166, 4719, 182326, 8927301, 529922002, 36988772211, 2969132797966, 269488306924833, 27291375956851546, 3050923148547318039, 373187615576953777510, 49580088565083198922845, 7109665420655116517351458, 1094492388113416460752513851

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)! * Stirling2(n,k).

a(n) ~ 3^(4*n) * LambertW(2*exp(1/3)/3)^(3*n + 1) * n^(n-1) / (sqrt(1 + LambertW(2*exp(1/3)/3)) * 2^(3*n + 1) * exp(n) * (3*LambertW(2*exp(1/3)/3) - 1)^(4*n + 1)). - Vaclav Kotesovec, Nov 07 2023

Mathematica

Table[1/(3*n+1)! * Sum[(3*n+k)! * StirlingS2[n, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 07 2023 *)

Prog

(PARI) a(n) = sum(k=0, n, (3*n+k)!*stirling(n, k, 2))/(3*n+1)!;

Crossrefs

Cf. A000670, A052894, A367134.

Cf. A367137, A367139.

Sequence in context: A004107 A180831 A361094 * A367139 A180819 A132874

Adjacent sequences: A367132 A367133 A367134 * A367136 A367137 A367138

Keyword

nonn

Author

Seiichi Manyama, Nov 06 2023

Status

approved