In a book I have met one interesting equation (without reference): $$\frac{m!}{n!}\sum_{i=0}^n(-1)^i{n\choose{i}}{x+m+n-i\choose{m}}=\begin{cases} x+n+1,\, if \,m=n+1 \\ 1,\, if \,m=n \\ 0,\,if\, m<n. \end{cases}$$. First question is as follows: is there a simple answer for this sum for $m>n$? The second question: how can I find a name of the author of this equation (to make a reference in a paper).