A368068 a(n) = Product_{i=1..n, j=1..n} (2*i^2 + 5*i*j + 2*j^2).

1, 9, 129600, 40327580160000, 1311346674278439321600000000, 13821139470331790817454891043295068160000000000, 114180111981355345833797461507302737916551512227408406118400000000000000

Offset: 0

Author

Vaclav Kotesovec, Dec 10 2023

Keywords

• nonn

Crossrefs

Cf. A324402, A368065.

Programs

Mathematica

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

Formula

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

a(n) = A324402(n)^2.

a(n) ~ A * 3^(9*n*(n+1)/2 + 11/12) * n^(2*n^2 - 11/12) / (Pi * 2^(2*n^2 + 3*n + 17/12) * exp(3*n^2 + 1/12)), where A is the Glaisher-Kinkelin constant A074962.