Question 187
Let $n$ be a natural number. Find the number of permutations of the set $\{1, 2, \dots, n\}$ such that for each $i = 1, 2, \dots, n$, the first $i$ numbers in the permutation are not larger than $i + 1$. For example, there are 4 such permutations for $n = 3$: $\{1, 2, 3\}$, $\{2, 1, 3\}$, $\{1, 3, 2\}$ and $\{2, 3, 1\}$.