I'm working with the following conditioned probability density

where are discrete variables, and .

What I need is to find the maximum likelihood value for N that maximize the probability to have a given R. The approach I've tried is the classical ML estimation, so I set

that gives

The problem is that now I'm not able to solve this equation for

Is there any other way to find an estimate of given a particular from the first conditioned probability? I need only an estimate so I can consider to make some approximations...but I need a closed form, I cannot resort to numerical methods.

Thanks in advance!