OFFSET
0,2
COMMENTS
In general, for d>0, Product_{k=1..n} (k^2 + d*n^2) ~ (d+1)^(n + 1/2) * exp(n*(sqrt(d)*(Pi - 2*arctan(sqrt(d))) - 2)) * n^(2*n) / sqrt(d). - Vaclav Kotesovec, Jan 06 2024
FORMULA
a(n) ~ 3^(n + 1/2) * exp(n*(sqrt(2)*arctan(2*sqrt(2)) - 2)) * n^(2*n) / sqrt(2).
MATHEMATICA
Table[Product[k^2 + 2*n^2, {k, 1, n}], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jan 01 2024
STATUS
approved