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 A355786 #11 Jul 18 2022 12:22:37
%S A355786 1,1,5,42,497,7620,143979,3241406,84847489,2534788296,85170416115,
%T A355786 3180919433802,130771002469953,5869920100483452,285705285804636411,
%U A355786 14989889385040915830,843420165009747027969,50664760467069168337680,3236433107379299238343779
%N A355786 E.g.f. satisfies A(x) = 1/(1 - 2*x)^(A(x)/2).
%F A355786 E.g.f.: exp( -LambertW(log(1-2*x)/2) ).
%F A355786 a(n) = Sum_{k=0..n} 2^(n-k) * (k+1)^(k-1) * |Stirling1(n,k)|.
%F A355786 From _Vaclav Kotesovec_, Jul 18 2022: (Start)
%F A355786 E.g.f.: 2*LambertW(log(1-2*x)/2) / log(1-2*x).
%F A355786 a(n) ~ 2^(n - 1/2) * n^(n-1) * exp(3/2 - n + 2*n*exp(-1)) / (exp(2*exp(-1)) - 1)^(n - 1/2). (End)
%o A355786 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(log(1-2*x)/2))))
%o A355786 (PARI) a(n) = sum(k=0, n, 2^(n-k)*(k+1)^(k-1)*abs(stirling(n, k, 1)));
%Y A355786 Cf. A052813, A355779.
%K A355786 nonn
%O A355786 0,3
%A A355786 _Seiichi Manyama_, Jul 17 2022