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 A362522 #19 Aug 05 2025 03:13:00
%S A362522 1,1,3,7,49,201,2491,14743,266337,2055889,49051891,466650471,
%T A362522 13873711633,156839920537,5591748678699,73222243463671,
%U A362522 3046762637864641,45346835284775073,2158148557098011107,35980450963558606279,1928292118820446611441
%N A362522 a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)^(k-1) / (k! * (n-2*k)!).
%H A362522 Seiichi Manyama, <a href="/A362522/b362522.txt">Table of n, a(n) for n = 0..416</a>
%H A362522 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362522 E.g.f.: exp(x - LambertW(-x^2)) = -LambertW(-x^2)/x^2 * exp(x).
%F A362522 a(n) ~ sqrt(2) * (exp(2*exp(-1/2)) + (-1)^n) * n^(n-1) / exp(n/2 + exp(-1/2) - 1). - _Vaclav Kotesovec_, Aug 05 2025
%o A362522 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-x^2))))
%Y A362522 Cf. A088957, A362523.
%Y A362522 Cf. A089461, A362347.
%K A362522 nonn,easy
%O A362522 0,3
%A A362522 _Seiichi Manyama_, Apr 23 2023