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

%I #15 Apr 11 2023 11:33:24

%S 1,1,3,19,185,2401,38731,745123,16630769,422157025,12005107091,

%T 377957000851,13048046175913,490052749100929,19890724260375515,

%U 867582126490694371,40467070835396193761,2009901604798183428673,105901641663222888913699

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

%F a(n) = n! * Sum_{k=0..n} (-3)^k * binomial(-(n-k)/3,k)/(n-k)! = n! * Sum_{k=0..n} 3^(n-k) * binomial(n-2*k/3-1,n-k)/k!.

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x/(1-3*x)^(1/3))))

%Y Cf. A321837, A362164, A362188.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Apr 11 2023