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%I #16 Apr 23 2023 02:06:55
%S 1,1,1,4,49,481,4471,57751,1036393,19939753,399150541,9082285741,
%T 237719388721,6759766432849,204408880370059,6672899023062091,
%U 236080878357745681,8926817568378582481,357421258163575234873,15158257732928974255993
%N E.g.f. satisfies A(x) = exp(x + x^3/2 * A(x)^3).
%H Seiichi Manyama, <a href="/A362479/b362479.txt">Table of n, a(n) for n = 0..393</a>
%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(-3*x^3/2 * exp(3*x))/3) = ( -2 * LambertW(-3*x^3/2 * exp(3*x))/(3*x^3) )^(1/3).
%F a(n) = n! * Sum_{k=0..floor(n/3)} (1/2)^k * (3*k+1)^(n-2*k-1) / (k! * (n-3*k)!).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-3*x^3/2*exp(3*x))/3)))
%Y Column k=3 of A362490.
%Y Cf. A362391.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Apr 21 2023
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