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 A355994 #18 Feb 16 2025 08:34:03
%S A355994 0,0,0,3,6,20,270,1764,12600,169560,1937880,22300740,349806600,
%T A355994 5556245760,89073856872,1678920566400,33550354656000,687175528253760,
%U A355994 15462823882213440,370285712520237360,9180722384533375200,242398467521271149760
%N A355994 Expansion of e.g.f. -LambertW(x^2/2 * log(1-x)).
%H A355994 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A355994 a(n) = n! * Sum_{k=1..floor(n/3)} k^(k-1) * |Stirling1(n-2*k,k)|/(2^k * (n-2*k)!).
%t A355994 With[{m = 25}, Range[0, m]! * CoefficientList[Series[-ProductLog[x^2/2 * Log[1 - x]], {x, 0, m}], x]] (* _Amiram Eldar_, Sep 24 2022 *)
%o A355994 (PARI) my(N=20, x='x+O('x^N)); concat([0, 0, 0], Vec(serlaplace(-lambertw(x^2/2*log(1-x)))))
%o A355994 (PARI) a(n) = n!*sum(k=1, n\3, k^(k-1)*abs(stirling(n-2*k, k, 1))/(2^k*(n-2*k)!));
%Y A355994 Cf. A052807, A355995, A357265.
%K A355994 nonn
%O A355994 0,4
%A A355994 _Seiichi Manyama_, Sep 24 2022