A367941 a(n) = Product_{i=1..n, j=1..n} (i^2 + 2*j^2).

1, 3, 1944, 4102777008, 140890630179993255936, 247470977313135626800897828778803200, 54132901224855040835735917614114353691165557521593139200

Offset: 0

Author

Vaclav Kotesovec, Dec 05 2023

Keywords

• nonn

Crossrefs

Cf. A324403, A367942, A367943, A367944.

Cf. A367542, A367543.

Programs

Mathematica

Table[Product[i^2+2*j^2, {i, 1, n}, {j, 1, n}], {n, 0, 8}]

Formula

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...