A368065 a(n) = Product_{i=1..n, j=1..n} (i^2 + 5*i*j + j^2).

1, 7, 44100, 3210672937500, 12804360424787610000000000, 8591751256288909159255104643281750000000000, 2333034616280404811605303958158227652934766912996000000000000000000

Offset: 0

Author

Vaclav Kotesovec, Dec 10 2023

Keywords

• nonn

Crossrefs

Cf. A367543, A324403, A367542, A079478^2, A368067, A368064, A368066.

Cf. A368068, A368069.

Programs

Mathematica

Table[Product[i^2 + 5*i*j + j^2, {i, 1, n}, {j, 1, n}], {n, 0, 7}]

Formula

a(n) ~ c * 7^(7*n*(n+1)/2) * ((5-sqrt(21))/2)^(sqrt(21)*n*(n+1)/2) * n^(2*n^2 - 4/3) / exp(3*n^2), where c = A368069.