A367138 - OEIS

%I #13 Nov 07 2023 11:28:25

%S 1,1,7,98,2096,60684,2221766,98488592,5129567208,307066395000,

%T 20775900638472,1567955813868960,130596146677118448,

%U 11899839375083061024,1177540373453616858240,125754589311488009416704,14416305655742615673941760,1765794816084642802179333120

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

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

%F 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

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

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

%Y Cf. A007840, A052802, A367139.

%Y Cf. A367134, A367136.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 06 2023