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 A362396 #12 Feb 16 2025 08:34:05
%S A362396 1,1,-1,-11,-11,381,2461,-21083,-449623,221113,99327961,862237641,
%T A362396 -24117649907,-612442461227,3958786971413,388794711373741,
%U A362396 2915530533136081,-239559177608638095,-6208842113295032015,118603625804273873809,8571701737898867135861
%N A362396 E.g.f. satisfies A(x) = exp(x - x^2 * A(x)).
%H A362396 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362396 E.g.f.: exp(x - LambertW(x^2 * exp(x))) = LambertW(x^2 * exp(x))/x^2.
%F A362396 a(n) = n! * Sum_{k=0..floor(n/2)} (-1)^k * (k+1)^(n-k-1) / (k! * (n-2*k)!).
%o A362396 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(x^2*exp(x)))))
%Y A362396 Column k=2 of A362394.
%Y A362396 Cf. A362430, A362431.
%Y A362396 Cf. A125500.
%K A362396 sign
%O A362396 0,4
%A A362396 _Seiichi Manyama_, Apr 20 2023