A367136 E.g.f. satisfies A(x) = 1/(1 - log(1 + x*A(x)^2)).

1, 1, 5, 50, 764, 15804, 413426, 13094864, 487323000, 20844584760, 1007739144312, 54343954158240, 3234285062655984, 210581685526690464, 14889759832273000320, 1136236597054802033664, 93074880409847175490560, 8146156595011083708521472

Offset: 0

Author

Seiichi Manyama, Nov 06 2023

Keywords

• nonn

Crossrefs

Cf. A006252, A198860, A367137.

Cf. A367134, A367138.

Programs

Mathematica

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

PARI

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

Formula

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

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