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 A367138 #13 Nov 07 2023 11:28:25
%S A367138 1,1,7,98,2096,60684,2221766,98488592,5129567208,307066395000,
%T A367138 20775900638472,1567955813868960,130596146677118448,
%U A367138 11899839375083061024,1177540373453616858240,125754589311488009416704,14416305655742615673941760,1765794816084642802179333120
%N A367138 E.g.f. satisfies A(x) = 1/(1 + log(1 - x*A(x)^2)).
%F A367138 a(n) = (1/(2*n+1)!) * Sum_{k=0..n} (2*n+k)! * |Stirling1(n,k)|.
%F A367138 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 A367138 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 A367138 (PARI) a(n) = sum(k=0, n, (2*n+k)!*abs(stirling(n, k, 1)))/(2*n+1)!;
%Y A367138 Cf. A007840, A052802, A367139.
%Y A367138 Cf. A367134, A367136.
%K A367138 nonn
%O A367138 0,3
%A A367138 _Seiichi Manyama_, Nov 06 2023