Can the formula $\binom{n}{k}\cdot\binom{n-k}{k}\cdot\binom{n-2k}{k}\cdots\binom{n-(m-1)k}{k}$, where $m = n/k$ be simplified into a smaller formula.

Question

I am using this as a step for proving lower bound for comparison based $k$ sorting using binary decision tree method. $k$ sorting means a list of size n is divided into $k$ blocks, and all elements of the preceding block are less than all elements in the succeeding block. But the $k$ elements in each block needed not be sorted.