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%I #7 Nov 14 2023 17:26:54
%S 1,30,819,22188,599976,16212420,437948784,11828393820,319437445365,
%T 8626198419930,232935493710231,6289845008414760,169838331029620344,
%U 4585907100958922088,123825507087143633976,3343423515649756142760,90275493748778836055964
%N a(n) = 27^n * Sum_{k=0..n} binomial(1/3, k)^2.
%C In general, for m>1, Sum_{k>=0} binomial(1/m,k)^2 = Gamma(1 + 2/m) / Gamma(1 + 1/m)^2.
%F a(n) ~ 4 * Pi * 3^(3*n + 1/2) / Gamma(1/3)^3.
%t Table[27^n*Sum[Binomial[1/3, k]^2, {k, 0, n}], {n, 0, 16}]
%Y Cf. A358364, A367330, A367331, A367333.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Nov 14 2023