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%I #13 May 06 2023 09:00:56
%S 1,1,13,173,3321,81529,2443333,86475493,3529941873,163260749681,
%T 8437633695741,481912844592541,30142773978386281,2049173019206244073,
%U 150443505029536707381,11862692305729094644949,999864950902004743707873,89709634016056661732903137
%N Expansion of e.g.f. exp(-x) / (1 + LambertW(-2*x)).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F G.f.: Sum_{k>=0} (2*k*x)^k / (1 + x)^(k+1).
%F a(n) = (-1)^n * Sum_{k=0..n} (-2*k)^k * binomial(n,k).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-x)/(1 + lambertw(-2*x))))
%Y Column k=2 of A362019.
%Y Cf. A062971, A362857.
%K nonn,easy
%O 0,3
%A _Seiichi Manyama_, May 05 2023