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 A355780 #16 Jul 17 2022 10:59:09
%S A355780 1,2,10,96,1352,25400,597816,16941568,561993344,21372060672,
%T A355780 916910785920,43817650647936,2308500130055808,132941831957885184,
%U A355780 8308594453077321984,560108109905112238080,40514005700203717945344,3129925644058623770173440
%N A355780 E.g.f. satisfies A(x) = (1 + x)^(2 * A(x)).
%F A355780 E.g.f.: exp( -LambertW(-2 * log(1+x)) ).
%F A355780 a(n) = Sum_{k=0..n} 2^k * (k+1)^(k-1) * Stirling1(n,k).
%F A355780 From _Vaclav Kotesovec_, Jul 17 2022: (Start)
%F A355780 E.g.f.: -LambertW(-2*log(1+x)) / (2*log(1+x)).
%F A355780 a(n) ~ sqrt(2) * n^(n-1) / ((exp(exp(-1)/2) - 1)^(n - 1/2) * exp(n - 3/2 + exp(-1)/4)). (End)
%o A355780 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-2*log(1+x)))))
%o A355780 (PARI) a(n) = sum(k=0, n, 2^k*(k+1)^(k-1)*stirling(n, k, 1));
%Y A355780 Cf. A033917, A351274, A355787.
%K A355780 nonn
%O A355780 0,2
%A A355780 _Seiichi Manyama_, Jul 16 2022