A367080 - OEIS

%I #32 Nov 07 2023 08:22:53

%S 1,1,5,50,766,15914,418548,13337624,499600848,21516318360,

%T 1047593782440,56903921842272,3411723783002016,223803339516120480,

%U 15944855840879771232,1226078375934824887680,101209861891840507123200,8926972851724904613537792

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

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

%F 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

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

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

%Y Cf. A138013, A367152.

%Y Cf. A367078, A367153.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 07 2023