What is $ \prod_{i=1}^n\prod_{j=1}^{n-i}i^2+j^2 $ ?
It feels like there should be some way to simplify this or calculate it more efficiently than iterating over each of the $\sim n^2/2$ points.
The inner product is a special case of $ \prod_{j=1}^Nj^2+k $ for which a special form exists in terms of the hyperbolic sine and gamma function, but I don't know how hard it would be to use this to compute the exact (integer) product.