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%I #15 Sep 24 2022 08:15:23
%S 0,0,0,0,4,10,20,35,1176,10164,58920,277365,4472380,69189406,
%T 772011604,6861855455,95279504880,1819310613800,30768119885136,
%U 430200439251369,6770486332450740,139958614722287410,3033142442978720380,58782387380290683571,1138026666874389737544
%N Expansion of e.g.f. -LambertW(x^3/6 * (1 - exp(x))).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F a(n) = n! * Sum_{k=1..floor(n/4)} k^(k-1) * Stirling2(n-3*k,k)/(6^k * (n-3*k)!).
%o (PARI) my(N=30, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(serlaplace(-lambertw(x^3/6*(1-exp(x))))))
%o (PARI) a(n) = n!*sum(k=1, n\4, k^(k-1)*stirling(n-3*k, k, 2)/(6^k*(n-3*k)!));
%Y Cf. A048802, A355181, A357267.
%Y Cf. A353999, A355180.
%K nonn
%O 0,5
%A _Seiichi Manyama_, Sep 24 2022