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 A362282 #19 Feb 16 2025 08:34:05
%S A362282 1,1,-3,-17,145,1401,-19619,-267833,5214273,91975825,-2292948899,
%T A362282 -49586832129,1506939887377,38595456391753,-1383612408628995,
%U A362282 -40951481342092649,1691614670048805121,56809502720559644577,-2656760323700732460227,-99810124102484722532465
%N A362282 a(n) = n! * Sum_{k=0..floor(n/2)} (-n)^k * binomial(n-k,k)/(n-k)!.
%H A362282 Seiichi Manyama, <a href="/A362282/b362282.txt">Table of n, a(n) for n = 0..394</a>
%H A362282 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362282 a(n) = A362277(n,2*n).
%F A362282 a(n) = n! * [x^n] exp(x - n*x^2).
%F A362282 E.g.f.: exp( sqrt( LambertW(2*x^2)/2 ) ) / (1 + LambertW(2*x^2)).
%o A362282 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sqrt(lambertw(2*x^2)/2))/(1+lambertw(2*x^2))))
%Y A362282 Cf. A362276, A362277, A362281.
%K A362282 sign
%O A362282 0,3
%A A362282 _Seiichi Manyama_, Apr 14 2023