%I #11 Apr 11 2023 11:34:18
%S 1,1,5,43,513,7781,142861,3075255,75879553,2110145833,65275127541,
%T 2222656864451,82595058938305,3325666654250253,144214230714973693,
%U 6700048267934377231,331988586859256529921,17475202293073669341905,973765103770578798536293
%N Expansion of e.g.f. exp(x/(1-3*x)^(2/3)).
%F a(n) = n! * Sum_{k=0..n} (-3)^k * binomial(-2*(n-k)/3,k)/(n-k)! = n! * Sum_{k=0..n} 3^(n-k) * binomial(n-k/3-1,n-k)/k!.
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x/(1-3*x)^(2/3))))
%Y Cf. A321837, A362164, A362205.
%K nonn,easy
%O 0,3
%A _Seiichi Manyama_, Apr 11 2023