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Expansion of e.g.f. exp(x/(1-3*x)^(2/3)).
1

%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