A367137 E.g.f. satisfies A(x) = 1/(1 - log(1 + x*A(x)^3)).

1, 1, 7, 101, 2248, 68024, 2608940, 121316796, 6633841608, 417181294704, 29665022908992, 2353675598751960, 206145540193974288, 19755830347828845360, 2056381966404400741920, 231034314706671715165824, 27865886237401381188422400, 3591366670194210901813749120

Offset: 0

Author

Seiichi Manyama, Nov 06 2023

Keywords

• nonn

Crossrefs

Cf. A006252, A198860, A367136.

Cf. A367135, A367139.

Programs

Mathematica

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

PARI

a(n) = sum(k=0, n, (3*n+k)!*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(2))^n * n^(n-1) / (sqrt(3*(1 + LambertW(3*exp(2)))) * exp(n) * (3 - LambertW(3*exp(2)))^(4*n + 1)). - Vaclav Kotesovec, Nov 07 2023