A367080 E.g.f. satisfies A(x) = 1 - log(1 - x*A(x)^2).

1, 1, 5, 50, 766, 15914, 418548, 13337624, 499600848, 21516318360, 1047593782440, 56903921842272, 3411723783002016, 223803339516120480, 15944855840879771232, 1226078375934824887680, 101209861891840507123200, 8926972851724904613537792

Offset: 0

Author

Seiichi Manyama, Nov 07 2023

Keywords

• nonn

Crossrefs

Cf. A138013, A367152.

Cf. A367078, A367153.

Programs

Mathematica

Table[(2*n)! * Sum[Abs[StirlingS1[n,k]]/(2*n-k+1)!, {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 07 2023 *)

PARI

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

Formula

a(n) = (2*n)! * Sum_{k=0..n} |Stirling1(n,k)|/(2*n-k+1)!.

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