This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A367080 #32 Nov 07 2023 08:22:53
%S A367080 1,1,5,50,766,15914,418548,13337624,499600848,21516318360,
%T A367080 1047593782440,56903921842272,3411723783002016,223803339516120480,
%U A367080 15944855840879771232,1226078375934824887680,101209861891840507123200,8926972851724904613537792
%N A367080 E.g.f. satisfies A(x) = 1 - log(1 - x*A(x)^2).
%F A367080 a(n) = (2*n)! * Sum_{k=0..n} |Stirling1(n,k)|/(2*n-k+1)!.
%F A367080 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 A367080 Table[(2*n)! * Sum[Abs[StirlingS1[n,k]]/(2*n-k+1)!, {k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Nov 07 2023 *)
%o A367080 (PARI) a(n) = (2*n)!*sum(k=0, n, abs(stirling(n, k, 1))/(2*n-k+1)!);
%Y A367080 Cf. A138013, A367152.
%Y A367080 Cf. A367078, A367153.
%K A367080 nonn
%O A367080 0,3
%A A367080 _Seiichi Manyama_, Nov 07 2023