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%I #34 Oct 26 2024 07:09:19
%S 1,6,51,450,4095,37908,354978,3351348,31833945,303822090,2910657321,
%T 27970777926,269484894081,2602002636540,25170322256010,
%U 243876058527132,2366251795228437,22987502934573762,223563791480714685,2176402892261301990,21206170582394740371
%N Expansion of 1/(1 - 9*x*(1 + x))^(2/3).
%F a(n) = 3*((3*n-1)*a(n-1) + (3*n-2)*a(n-2))/n for n > 1.
%F a(n) = Sum_{k=0..n} (-9)^k * binomial(-2/3,k) * binomial(k,n-k).
%F a(n) ~ (3 + sqrt(13))^(n + 2/3) * 3^n / (Gamma(2/3) * 13^(1/3) * n^(1/3) * 2^(n + 2/3)). - _Vaclav Kotesovec_, Oct 26 2024
%o (PARI) a(n) = sum(k=0, n, (-9)^k*binomial(-2/3, k)*binomial(k, n-k));
%Y Cf. A180400, A377260, A377261.
%Y Cf. A377233.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Oct 21 2024