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 A361213 #22 Feb 16 2025 08:34:05
%S A361213 1,2,8,68,848,14192,298048,7546016,223792640,7612381952,292216807424,
%T A361213 12497875215872,589392367925248,30386736933804032,1700376343771136000,
%U A361213 102641314849948602368,6648428846464054919168,459977466799800897437696
%N A361213 E.g.f. satisfies A(x) = exp( 2*x*A(x) / (1+x) ).
%H A361213 Winston de Greef, <a href="/A361213/b361213.txt">Table of n, a(n) for n = 0..360</a>
%H A361213 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A361213 a(n) = (-1)^n * n! * Sum_{k=0..n} (-2)^k * (k+1)^(k-1) * binomial(n-1,n-k)/k!.
%F A361213 E.g.f.: exp ( -LambertW(-2*x/(1+x)) ).
%F A361213 E.g.f.: -(1+x)/(2*x) * LambertW(-2*x/(1+x)).
%F A361213 a(n) ~ (2*exp(1) - 1)^(n + 1/2) * n^(n-1) / (sqrt(2) * exp(n - 1/2)). - _Vaclav Kotesovec_, Nov 10 2023
%o A361213 (PARI) a(n) = (-1)^n*n!*sum(k=0, n, (-2)^k*(k+1)^(k-1)*binomial(n-1, n-k)/k!);
%o A361213 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-2*x/(1+x)))))
%o A361213 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-(1+x)/(2*x)*lambertw(-2*x/(1+x))))
%Y A361213 Cf. A335945, A361214.
%Y A361213 Cf. A361068, A361193.
%K A361213 nonn
%O A361213 0,2
%A A361213 _Seiichi Manyama_, Mar 04 2023