A367138 E.g.f. satisfies A(x) = 1/(1 + log(1 - x*A(x)^2)).

1, 1, 7, 98, 2096, 60684, 2221766, 98488592, 5129567208, 307066395000, 20775900638472, 1567955813868960, 130596146677118448, 11899839375083061024, 1177540373453616858240, 125754589311488009416704, 14416305655742615673941760, 1765794816084642802179333120

Offset: 0

Author

Seiichi Manyama, Nov 06 2023

Keywords

• nonn

Crossrefs

Cf. A007840, A052802, A367139.

Cf. A367134, A367136.

Programs

Mathematica

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

PARI

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