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%I #5 Mar 08 2019 15:53:05
%S 2,8,2400,1247616000,47391629172572160000,
%T 5433273487668074503912921497600000000,
%U 84476763043100284572577776893541858819157327099409203200000000
%N a(n) = Product_{i=0..n, j=0..n} (binomial(2*i, j) + binomial(2*j, i)).
%F a(n) ~ c * d^n * exp(2*n^3/3 + 9*n^2/4) / (2^(n^2) * Pi^(n^2/2) * n^(n^2/2 + 5*n/6 - alfa)), where
%F d = 2.631186542501652610455988727776308850706336468478433795517960445788077147...
%F alfa = 0.094637735750903047180156176044316953484876143616883847755312100285099...
%F c = 0.121223472988717836553569221604723373713338356783096...
%t Table[Product[Binomial[2*i, j] + Binomial[2*j, i], {i, 0, n}, {j, 0, n}], {n, 0, 7}]
%Y Cf. A000984, A007685, A324566, A324568.
%K nonn
%O 0,1
%A _Vaclav Kotesovec_, Mar 07 2019
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