Trying to code a tricky double summation

So I'm trying to write code that calculates the following:

I have two functions of the same two variables, call them D(x,y) and T(x,y)

I'm trying to write a function that accepts inputs x,y,z and outputs:

Sum_{i=0}^min(x,y) Sum_{k=0}^(x-i) (-1)^k D(2x-2k-2i,2y+k-2l) * T(2x-2k-2l,2y+k-2i)^(z/2)

So, there are two summations, the outer one takes the sum from i=0 up to min(x,y), and the inner sum takes the summation of terms from k=0 up to x-i

The inner sum isn't as complicated as it looks, it has a (-1)^k at the start and then just multiples the functions D(a,b) and T(a,b)^(z/2) where a and b depend on both where you are in the indexing of your outer summation and inner summation

This is a much harder proram than I have written before, so tips, insights, general advice, and even completed code are welcome!! Thanks for your time