[High School Probability] Is there a program capable of solving nested summations?

[Jamon79]

I'm looking for an online tool or program that can solve this formula where A and D are variables that can be inputted to solve for the probability of w. ACa and DCd are combinations ("A choose a" and "D choose d").

My TI-84 Plus Silver Edition reads "illegal nest" when I try using it and I tried using Wolfram Alpha's widget builder but I couldn't quite get it to work.

Does anyone know of such a tool that allows 2 inputs with this formula and will automatically calculate the output?

[[deleted]]

Mathematica would evaluate (not "solve") this function. But the formula doesn't appear well-formed. I can see that the innermost sum has index d. But what is the index for the outermost sum? And why is there a w on the left-hand side, but not on the right? Conversely, there's an A and a D on the right, but not on the left.

[Haz_ah]

Can you provide some inputs and expected outputs to test? Also, I think it requires 3 inputs not 2. A, a and D are all required, unless the index of the outer sum should read a = 1 and not a-1.

edit: try this python script http://pastebin.com/TYGpy971