I've been able to work through most of the problem so far, so I'm only posting what's relevant:

$\displaystyle X_1, X_2, ..., X_n \sim Poisson(\theta)$ and $\displaystyle Y = \sum{X_i}$

What I need help with is calculating: $\displaystyle E(\frac{n}{Y+1})$

It seems like it ought to be easy, but I'm drawing a blank. Is using the mgf the strategy I should be looking at? If so, how?