Let $\pi = \pi_{1}\pi_{2}\ldots\ldots\pi_{n}$ be a permutation of the numbers $1,2,3,\ldots,n$. We say $\pi$ has its first ascent at position $k < n$ if $\pi_{1} > \pi_{2} \ldots > \pi_{k}$ and $\pi_{k} < \pi_{k+1}$. If $\pi_{1} > \pi_{2} > \ldots > \pi_{n-1} > \pi_{n}$ we say $\pi$ has its first ascent in position $n$. For example when $n = 4$ the permutation 2134 has its first ascent at position 2.
The number of permutations which have their first ascent at position $k$ is ......