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 A362776 #13 Feb 16 2025 08:34:05
%S A362776 1,1,9,127,2601,70981,2433673,100697787,4886085137,272168650441,
%T A362776 17121437245161,1200717094233559,92892754255837561,
%U A362776 7859587210132504653,721996671783802854377,71564871858940414914451,7613407794191946986893857,865285095267929315207801233
%N A362776 E.g.f. satisfies A(x) = exp( x/(1-x)^2 * A(x)^2 ).
%H A362776 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362776 E.g.f.: exp( -LambertW(-2*x/(1-x)^2)/2 ).
%F A362776 a(n) = n! * Sum_{k=0..n} (2*k+1)^(k-1) * binomial(n+k-1,n-k)/k!.
%F A362776 From _Vaclav Kotesovec_, Nov 10 2023: (Start)
%F A362776 E.g.f.: (1-x) * sqrt(-LambertW(-2*x/(1-x)^2) / (2*x)).
%F A362776 a(n) ~ sqrt(-sqrt(1 + 2*exp(-1)) + 1 + 2*exp(-1)) * n^(n-1) / (sqrt(2) * (-1 + sqrt(1 + 2*exp(-1)))^(3/2) * (-sqrt(1 + 2*exp(-1)) + 1 + exp(-1))^(n - 1/2) * exp(2*n - 1/2)). (End)
%o A362776 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-2*x/(1-x)^2)/2)))
%Y A362776 Cf. A082579, A362775.
%Y A362776 Cf. A361065.
%K A362776 nonn
%O A362776 0,3
%A A362776 _Seiichi Manyama_, May 02 2023