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I'd like to model proportion of certain species in a popualtion with Borel-Tanner distribution: $\frac{e^{-m}m^{m-1}}{m!}$, its support is defined on $\{1,2,...\}$, but I need finite bound. Could anyone help me with finding the finite sum $\sum_{m=1}^{n}\frac{e^{-m}m^{m-1}}{m!}$?

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The Borel-Tanner distribution is not given by the formula you write. Furthermore the sum of the series of general term $\mathrm{e}^{-m}m^m/m!$ is infinite and in particular, not $1$. –  Did May 21 '11 at 11:37
    
I edited it accordingly –  sigma.z.1980 May 22 '11 at 0:26
    
If the (modified) weights you consider sum to $1$, you could show why. –  Did May 22 '11 at 6:27
    
I need the sum $\sum_{m=1}^{\mu} \frac{e^{-m}m^{m-1}}{m!}$, and I haven't found it so far –  sigma.z.1980 May 24 '11 at 1:21

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