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 A355993 #17 Feb 16 2025 08:34:03
%S A355993 0,0,0,0,4,10,40,210,8064,70560,640800,6375600,189383040,3165402240,
%T A355993 48879754560,762766804800,21652937349120,525738717504000,
%U A355993 11796584629939200,259139188966694400,7842638783736115200,240231375437935795200,7066934411387842252800
%N A355993 Expansion of e.g.f. -LambertW(x^3 * log(1-x))/6.
%H A355993 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A355993 a(n) = (n!/6) * Sum_{k=1..floor(n/4)} k^(k-1) * |Stirling1(n-3*k,k)|/(n-3*k)!.
%t A355993 With[{m = 25}, Range[0, m]! * CoefficientList[Series[-ProductLog[x^3 * Log[1 - x]]/6, {x, 0, m}], x]] (* _Amiram Eldar_, Sep 24 2022 *)
%o A355993 (PARI) my(N=30, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(serlaplace(-lambertw(x^3*log(1-x)))/6))
%o A355993 (PARI) a(n) = n!*sum(k=1, n\4, k^(k-1)*abs(stirling(n-3*k, k, 1))/(n-3*k)!)/6;
%Y A355993 Cf. A052807, A355874, A357265.
%K A355993 nonn
%O A355993 0,5
%A A355993 _Seiichi Manyama_, Sep 24 2022