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

0,3

Links

Table of n, a(n) for n=0..17.

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

Mathematica

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

Prog

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

Crossrefs

Cf. A138013, A367080.

Sequence in context: A142358 A210684 A367137 * A357334 A329239 A020477

Adjacent sequences: A367149 A367150 A367151 * A367153 A367154 A367155

Keyword

nonn

Author

Seiichi Manyama, Nov 07 2023

Status

approved