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%I #11 Apr 22 2023 10:31:51
%S 1,1,1,-1,-31,-319,-2279,-4199,269473,7155233,114846641,920526641,
%T -18415853279,-1115017249631,-31675298017271,-526379460621559,
%U 2394778195929281,603748739138745281,27895091311964499553,769764386129113157473,6164705700089328588481
%N E.g.f. satisfies A(x) = exp(x - x^3/3 * A(x)^3).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F E.g.f.: exp(x - LambertW(x^3 * exp(3*x))/3) = ( LambertW(x^3 * exp(3*x))/x^3 )^(1/3).
%F a(n) = n! * Sum_{k=0..floor(n/3)} (-1/3)^k * (3*k+1)^(n-2*k-1) / (k! * (n-3*k)!).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(x^3*exp(3*x))/3)))
%Y Cf. A362492, A362494.
%Y Cf. A362478.
%K sign
%O 0,5
%A _Seiichi Manyama_, Apr 22 2023
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