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 A362775 #16 Feb 16 2025 08:34:05
%S A362775 1,1,7,70,965,17216,379207,9969772,305154313,10668593008,419714689931,
%T A362775 18358646058644,884070662867053,46486344447041032,2650567497877525423,
%U A362775 162908800485532424236,10737607698626311094033,755571950776792829919968
%N A362775 E.g.f. satisfies A(x) = exp( x/(1-x)^2 * A(x) ).
%H A362775 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362775 E.g.f.: exp( -LambertW(-x/(1-x)^2) ).
%F A362775 a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(n+k-1,n-k)/k!.
%F A362775 From _Vaclav Kotesovec_, Nov 10 2023: (Start)
%F A362775 E.g.f.: -LambertW(-x/(1-x)^2) * (1-x)^2 / x.
%F A362775 a(n) ~ 2^(n + 1/2) * sqrt(1 + 4*exp(-1) - sqrt(1 + 4*exp(-1))) * n^(n-1) / ((-1 + sqrt(1 + 4*exp(-1)))^(3/2) * (1 + 2*exp(-1) - sqrt(1 + 4*exp(-1)))^(n - 1/2) * exp(2*n-1)). (End)
%o A362775 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x/(1-x)^2))))
%Y A362775 Cf. A082579, A362776.
%Y A362775 Cf. A052868, A361065.
%K A362775 nonn
%O A362775 0,3
%A A362775 _Seiichi Manyama_, May 02 2023