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Expansion of 1/(1 + x * (1-9*x)^(1/3)).
2

%I #14 Apr 10 2023 10:52:01

%S 1,-1,4,2,46,221,1627,11312,83704,631433,4868920,38137757,302694082,

%T 2428593929,19664122513,160464212831,1318266144163,10893680220326,

%U 90486907158265,755060334587576,6326283013232206,53199259567645709,448846559987031064

%N Expansion of 1/(1 + x * (1-9*x)^(1/3)).

%F a(n) = (-1)^n * Sum_{k=0..n} 9^k * binomial((n-k)/3,k).

%F a(n) ~ 3^(2*n-3) / (Gamma(2/3) * n^(4/3)). - _Vaclav Kotesovec_, Apr 10 2023

%o (PARI) my(N=30, x='x+O('x^N)); Vec(1/(1+x*(1-9*x)^(1/3)))

%Y Cf. A039834, A362154.

%Y Cf. A004987, A362157, A362162.

%K sign,easy

%O 0,3

%A _Seiichi Manyama_, Apr 09 2023