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 A354288 #15 Oct 13 2022 14:29:33
%S A354288 1,2,10,72,664,7440,97712,1468768,24825184,465516672,9582002688,
%T A354288 214642099584,5195322070656,135064965744384,3752151488840448,
%U A354288 110892824334154752,3473236656134243328,114893633354895538176,4002000861023966189568,146388324613230926979072
%N A354288 Expansion of e.g.f. (1 + x)^(2/(1 - 2 * log(1+x))).
%F A354288 a(0) = 1; a(n) = Sum_{k=1..n} A088501(k) * binomial(n-1,k-1) * a(n-k).
%F A354288 a(n) = Sum_{k=0..n} 2^k * A000262(k) * Stirling1(n,k).
%F A354288 a(n) ~ exp(-7/8 + 1/(4*(exp(1/2) - 1)) + sqrt((2*n)/(exp(1/2) - 1))*exp(1/4) - n) * n^(n - 1/4) / (2^(3/4) * (exp(1/2) - 1)^(n + 1/4)). - _Vaclav Kotesovec_, May 23 2022
%t A354288 With[{nn=20},CoefficientList[Series[(1+x)^(2/(1-2Log[1+x])),{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Oct 13 2022 *)
%o A354288 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((1+x)^(2/(1-2*log(1+x)))))
%o A354288 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, sum(k=0, j, 2^k*k!*stirling(j, k, 1))*binomial(i-1, j-1)*v[i-j+1])); v;
%Y A354288 Cf. A088819, A354289.
%Y A354288 Cf. A000262, A088501, A354286, A354290.
%K A354288 nonn
%O A354288 0,2
%A A354288 _Seiichi Manyama_, May 23 2022