Sum over k of r-kt Choose k by r over r-kt by s-(n-k)t Choose n-k by s over s-(n-k)t

Theorem
For $n \in \Z_{\ge 0}$:


 * $\displaystyle \sum_k A_k \left({r, t}\right) A_{n - k} \left({s, t}\right) = A_n \left({r + s, t}\right)$

where $A_n \left({x, t}\right)$ is the polynomial of degree $n$ defined as:
 * $A_n \left({x, t}\right) = \dbinom {x - n t} n \dfrac x {x - n t}$

where $x \ne n t$.