Thank you both for your feedback.
I wonder if a better tack would be to check if one (or more) of these polynomials (in three variables: n,d and k) can be factored into two smaller polynomials say g(n,d,k) and h(n,d,k).
By setting g(n,d,k) = h(n,d,k), perhaps I make some progress simplifying it(say by using substitution).
Is there a tool (preferably free or online) that can check if a multivariable polynomial is irreducible. I have PARI installed but it can only check/factor singlevariable polynomials.
Could Magma handle something like that? I tried Wolfram Alpha but it exceeded the upper bound on query length.
