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A368067
a(n) = Product_{i=1..n, j=1..n} (i^2 + 3*i*j + j^2).
3
1, 5, 12100, 188898484500, 91554454518735288960000, 4263420404009649597344435073399120000000, 46073465749493255153019723901007197815549903333795840000000000
OFFSET
0,2
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.
MATHEMATICA
Table[Product[i^2 + 3*i*j + j^2, {i, 1, n}, {j, 1, n}], {n, 0, 7}]
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Dec 10 2023
STATUS
approved