A367136 - OEIS

%I #14 Nov 07 2023 11:18:03

%S 1,1,5,50,764,15804,413426,13094864,487323000,20844584760,

%T 1007739144312,54343954158240,3234285062655984,210581685526690464,

%U 14889759832273000320,1136236597054802033664,93074880409847175490560,8146156595011083708521472

%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(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

%t Table[1/(2*n+1)! * Sum[(2*n+k)! * 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)!*stirling(n, k, 1))/(2*n+1)!;

%Y Cf. A006252, A198860, A367137.

%Y Cf. A367134, A367138.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 06 2023