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%I #7 Nov 14 2023 17:26:50
%S 1,30,846,23430,643635,17601732,480016620,13065872292,355170348720,
%T 9644965082940,261716257738980,7097365769203260,192376104782028120,
%U 5212313820585819540,141177183151026767580,3822747528826291049460,103486045894075138514445
%N a(n) = 27^n * Sum_{k=0..n} binomial(-1/3, k)^2.
%C Compare with A358365: Sum_{k>=0} binomial(-1/3, k)^2 converges, but Sum_{k>=0} binomial(-1/2, k)^2 diverges.
%C In general, for m>2, Sum_{k>=0} binomial(-1/m,k)^2 = Gamma(1 - 2/m) / Gamma(1 - 1/m)^2.
%F a(n) ~ Gamma(1/3)^3 * 3^(3*n+1) / (4*Pi^2).
%t Table[27^n*Sum[Binomial[-1/3, k]^2, {k, 0, n}], {n, 0, 16}]
%Y Cf. A358365, A367330, A367331, A367332.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Nov 14 2023
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