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 A355874 #25 Feb 16 2025 08:34:03
%S A355874 0,0,0,3,6,20,450,3024,21840,449280,5690160,68579280,1491462720,
%T A355874 27798076800,485405784864,11821894207200,285057334598400,
%U A355874 6578025489584640,183420564173141760,5342163886869062400,152988752430721267200,4897735504358795965440
%N A355874 Expansion of e.g.f. -LambertW(x^2 * log(1-x))/2.
%H A355874 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A355874 a(n) = (n!/2) * Sum_{k=1..floor(n/3)} k^(k-1) * |Stirling1(n-2*k,k)|/(n-2*k)!.
%t A355874 With[{m = 25}, Range[0, m]! * CoefficientList[Series[-ProductLog[x^2 * Log[1 - x]]/2, {x, 0, m}], x]] (* _Amiram Eldar_, Sep 24 2022 *)
%o A355874 (PARI) my(N=20, x='x+O('x^N)); concat([0, 0, 0], Vec(serlaplace(-lambertw(x^2*log(1-x)))/2))
%o A355874 (PARI) a(n) = n!*sum(k=1, n\3, k^(k-1)*abs(stirling(n-2*k, k, 1))/(n-2*k)!)/2;
%Y A355874 Cf. A052807, A355993, A357265.
%Y A355874 Cf. A355179.
%K A355874 nonn
%O A355874 0,4
%A A355874 _Seiichi Manyama_, Sep 24 2022