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 A362395 #12 Feb 16 2025 08:34:05
%S A362395 1,1,0,-5,-14,56,736,1114,-45156,-428660,2004796,82797716,446153632,
%T A362395 -13593781928,-276074700264,701782138576,107474258830096,
%U A362395 1263010302870608,-30208216250914352,-1146149464640506928,-2087509382334856224,703335832718961413056
%N A362395 E.g.f. satisfies A(x) = exp(x - x^2/2 * A(x)).
%H A362395 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362395 E.g.f.: exp(x - LambertW(x^2/2 * exp(x))) = 2 * LambertW(x^2/2 * exp(x))/x^2.
%F A362395 a(n) = n! * Sum_{k=0..floor(n/2)} (-1/2)^k * (k+1)^(n-k-1) / (k! * (n-2*k)!).
%o A362395 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(x^2/2*exp(x)))))
%Y A362395 Column k=1 of A362394.
%Y A362395 Cf. A143740.
%K A362395 sign
%O A362395 0,4
%A A362395 _Seiichi Manyama_, Apr 20 2023