A368067 a(n) = Product_{i=1..n, j=1..n} (i^2 + 3*i*j + j^2).

1, 5, 12100, 188898484500, 91554454518735288960000, 4263420404009649597344435073399120000000, 46073465749493255153019723901007197815549903333795840000000000

Offset: 0

Author

Vaclav Kotesovec, Dec 10 2023

Keywords

• nonn

Crossrefs

Cf. A367543, A324403, A367542, A079478^2, A368064, A368065, A368066.

Programs

Mathematica

Table[Product[i^2 + 3*i*j + j^2, {i, 1, n}, {j, 1, n}], {n, 0, 7}]

Formula

a(n) ~ 5^(5*n*(n+1)/2 + 1/2) * n^(2*n^2 - 1) / (2 * Pi * exp(3*n^2) * phi^(sqrt(5)*(n*(n+1) + 1/6) - 1/2)), where phi = A001622 is the golden ratio.