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 A355179 #30 Aug 07 2025 12:34:46
%S A355179 0,0,0,3,6,10,375,2541,11788,317556,4238685,37921015,909616026,
%T A355179 18283276518,261259582675,6360432558585,164704011195480,
%U A355179 3332419310132776,88606184592031353,2713050497589230763,71412977041725823750,2144089948615678382970
%N A355179 Expansion of e.g.f. -LambertW(x^2 * (1 - exp(x)))/2.
%H A355179 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A355179 a(n) = (n!/2) * Sum_{k=1..floor(n/3)} k^(k-1) * Stirling2(n-2*k,k)/(n-2*k)!.
%t A355179 With[{nn=30},CoefficientList[Series[(-LambertW[x^2 (1-Exp[x])])/2,{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Aug 07 2025 *)
%o A355179 (PARI) my(N=20, x='x+O('x^N)); concat([0, 0, 0], Vec(serlaplace(-lambertw(x^2*(1-exp(x)))/2)))
%o A355179 (PARI) a(n) = n!*sum(k=1, n\3, k^(k-1)*stirling(n-2*k, k, 2)/(n-2*k)!)/2;
%Y A355179 Cf. A048802, A355180, A357267.
%K A355179 nonn
%O A355179 0,4
%A A355179 _Seiichi Manyama_, Sep 24 2022