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 A355788 #10 Jul 18 2022 12:26:58
%S A355788 1,1,5,38,409,5772,101227,2126966,52153185,1462998168,46232500275,
%T A355788 1625693415898,62972266884721,2664713395180228,122315552809623323,
%U A355788 6053803331878334590,321389617069279569345,18218906261462603910704,1098415656103838009681123
%N A355788 E.g.f. satisfies log(A(x)) = (exp(2*x) - 1) * A(x)/2.
%F A355788 E.g.f.: exp( -LambertW((1 - exp(2*x))/2) ).
%F A355788 a(n) = Sum_{k=0..n} 2^(n-k) * (k+1)^(k-1) * Stirling2(n,k).
%F A355788 From _Vaclav Kotesovec_, Jul 18 2022: (Start)
%F A355788 E.g.f.: 2*LambertW((1 - exp(2*x))/2) / (1 - exp(2*x)).
%F A355788 a(n) ~ 2^(n - 1/2) * sqrt(exp(1) + 2) * n^(n-1) / (exp(n-1) * (log(exp(1) + 2) - 1)^(n - 1/2)). (End)
%o A355788 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw((1-exp(2*x))/2))))
%o A355788 (PARI) a(n) = sum(k=0, n, 2^(n-k)*(k+1)^(k-1)*stirling(n, k, 2));
%Y A355788 Cf. A052880, A355781.
%K A355788 nonn
%O A355788 0,3
%A A355788 _Seiichi Manyama_, Jul 17 2022