Consecutive product sum

Can you solve this without pen and paper?

Suppose $r \gt 0$ is a fixed positive integer.

Can you give a formula (in terms of $n$ and $r$) for


$$\sum_{k=r}^{n} \left( \prod_{j=0}^{r} (k-j) \right)$$

i.e.

$$\sum_{k=r}^{n} k(k-1)(k-2)\dots(k-r)$$


[Solution]