A question on Poisson distribution

Hi,

Let X1 and X2 be Poisson distributed variables with the same mean m and Y be defined as multiplication of X1 and X2 (Y=X1X2). How can i obtain the probability function (pf) of Y http://www.talkstats.com/images/smilies/confused.gif

I tried to find it such that

I define the following Y1=X1X2 and Y2=X2 so X1=Y1/Y2 and X2=Y2. When i put Y1/Y2 in place of X1 in the joint pf of X1 and X2, there is an unidentifiability for Y2=0 because denominator has such a term: (Y1/Y2)!.

Thanks in advance...