Expressions in a probability problem look like this (see attached image).

P(d=6)

P(d=8)

P(d=10)

P(d=12) etc.

Each expression contains (d-6)/2 nested sums, each one nested into the former. The lower limit of each nested sum depends on the present value of the summation index of its parent sum.

I have attempted to describe the general formula P(d=d). How could this be programmed into mathematical software, e.g. Maple 12, because I am interested in evaluating P(d=d) for very high values of d?

(E.g. The formula for P(d=100) would contain (100-6)/2 = 47 sums, each one nested into its parent. It would take a long time to program that into a computer! )

So how can I describe this general formula in a way so that I can assign a value for d and simply execute a little program which builds the appropriate expression and evaluates it?