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 A361916 #34 Feb 16 2025 08:34:05
%S A361916 1,1,-1,-5,25,161,-1409,-12221,158705,1733185,-30136769,-397326709,
%T A361916 8696945929,134416055905,-3555479651905,-63044502191789,
%U A361916 1957884163020001,39178556553643649,-1398250387206450305,-31169265056007817445,1257498026543130033401
%N A361916 a(n) = n! * Sum_{k=0..floor(n/2)} (-1)^k * (k+1)^(k-1) / (k! * (n-2*k)!).
%H A361916 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A361916 E.g.f.: exp(x - LambertW(x^2)) = LambertW(x^2)/x^2 * exp(x).
%o A361916 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(x^2))))
%Y A361916 Cf. A105785, A361917, A362522.
%K A361916 sign,easy
%O A361916 0,4
%A A361916 _Seiichi Manyama_, Apr 24 2023