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[tex]\displaystyle\prod_{k=1}^x{(n+k)}=\displaystyle\sum_{LB}^{UB}F[/tex]

Where LB and UB are the respective lower and upper bounds. I'm assuming it has something to do with binomial coefficients since the obvious

[tex]{(a+b)}^n=\displaystyle\sum_{k=0}^{n}{\binom{n}{k}a^{n-k}b^{k}}[/tex]