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%I #7 Dec 07 2023 02:20:26
%S 1,3,1944,4102777008,140890630179993255936,
%T 247470977313135626800897828778803200,
%U 54132901224855040835735917614114353691165557521593139200
%N a(n) = Product_{i=1..n, j=1..n} (i^2 + 2*j^2).
%F a(n) ~ c * n^(2*n^2 - 1/2) * 3^(n*(n+1)) * 2^(-n/2) * exp(n*(n+1)*(Pi - arctan(sqrt(2))) / sqrt(2) - 3*n^2) , where c = 0.4690673220228472212446336926899602910226601891141458824921925169726804439...
%t Table[Product[i^2+2*j^2, {i, 1, n}, {j, 1, n}], {n, 0, 8}]
%Y Cf. A324403, A367942, A367943, A367944.
%Y Cf. A367542, A367543.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Dec 05 2023
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