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A closed form of a summation or the taylor series expansion of some function with a closed form?
Let $Z_N = \displaystyle{\sum_{k+j\leq N}} \frac{N!N^{k+j}}{N^{N+1}}\frac{u^kv^j}{k!j!}\binom{N-j}{N-j-k}$ where $u$ and $v$ are two unknowns.
My question is: Is there a closed-form for $Z_N$ or is $...
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