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 A362572 #20 Aug 05 2025 07:47:34
%S A362572 1,1,1,4,13,76,421,3361,26209,267688,2689201,33579811,412800961,
%T A362572 6103089994,88754687113,1517513934301,25487131948321,495009722435176,
%U A362572 9430633148123809,205154208873930763,4371962638221712801,105330237499426955926
%N A362572 E.g.f. satisfies A(x) = exp(x * A(x)^(x/2)).
%H A362572 Seiichi Manyama, <a href="/A362572/b362572.txt">Table of n, a(n) for n = 0..439</a>
%H A362572 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362572 E.g.f.: (-2 * LambertW(-x^2/2) / x^2)^(2/x) = exp(-2 * LambertW(-x^2/2) / x) = exp(x * exp(-LambertW(-x^2/2))).
%F A362572 a(n) = n! * Sum_{k=0..floor(n/2)} ((n-k)/2)^k * binomial(n-k-1,k)/(n-k)!.
%F A362572 E.g.f.: Sum_{k>=0} (k*x/2 + 1)^(k-1) * x^k / k!.
%F A362572 a(n) ~ (exp(sqrt(2)*exp(1/2)) - (-1)^n*exp(-sqrt(2)*exp(1/2))) * n^(n-1) / (2^(n/2 - 1) * exp((n-1)/2)). - _Vaclav Kotesovec_, Aug 05 2025
%o A362572 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*exp(-lambertw(-x^2/2)))))
%Y A362572 Cf. A000272, A362573.
%Y A362572 Cf. A361777.
%K A362572 nonn
%O A362572 0,4
%A A362572 _Seiichi Manyama_, Apr 25 2023