A367152 E.g.f. satisfies A(x) = 1 - log(1 - x*A(x)^3).

1, 1, 7, 101, 2250, 68184, 2619822, 122071704, 6689791392, 421670267136, 30055781201520, 2390512621714656, 209893714832795760, 20165895195283566000, 2104433775967024226592, 237043144515185017456320, 28664975599576485530851584, 3704019298858867019823244800

Offset: 0

Author

Seiichi Manyama, Nov 07 2023

Keywords

• nonn

Crossrefs

Cf. A138013, A367080.

Programs

Mathematica

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

PARI

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

Formula

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

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