Solution to a Modified Binomial Probability Distribution

I could use help determining whether the following can be solved analytically.

I have an equation .

Notice this equation is the binomial probability distribution from c to Q (as opposed to going from 0 to Q), and it is multiplied by .

I understand that simplifies to . Can a similar simplification be made to the equation I've presented above? Any thoughts on how I might go about it?

Thank you for your help.

Josh

Re: Solution to a Modified Binomial Probability Distribution