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).