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 A354240 #23 Jul 04 2025 18:57:04
%S A354240 1,2,10,88,1080,17088,330528,7558752,199487136,5967529152,
%T A354240 199533657792,7374470138880,298520508249600,13135454575464960,
%U A354240 624240306760343040,31864146725023718400,1738698154646011499520,100996114388088994007040
%N A354240 Expansion of e.g.f. 1/sqrt(1 - 4 * log(1+x)).
%F A354240 E.g.f.: Sum_{k>=0} binomial(2*k,k) * log(1+x)^k.
%F A354240 a(n) = Sum_{k=0..n} (2*k)! * Stirling1(n,k)/k!.
%F A354240 a(n) ~ n^n / (sqrt(2) * (exp(1/4)-1)^(n + 1/2) * exp(n - 1/8)). - _Vaclav Kotesovec_, Jun 04 2022
%F A354240 a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * (4 - 2*k/n) * (k-1)! * binomial(n,k) * a(n-k). - _Seiichi Manyama_, Sep 11 2023
%t A354240 With[{nn=20},CoefficientList[Series[1/Sqrt[1-4Log[1+x]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jul 04 2025 *)
%o A354240 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1-4*log(1+x))))
%o A354240 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, binomial(2*k, k)*log(1+x)^k)))
%o A354240 (PARI) a(n) = sum(k=0, n, (2*k)!*stirling(n, k, 1)/k!);
%Y A354240 Cf. A009199, A320343, A354241, A354242, A354243.
%K A354240 nonn
%O A354240 0,2
%A A354240 _Seiichi Manyama_, May 20 2022