Question 26
Let $n$ be a positive integer. Call a sequence of positive integers $a_{1}, a_{2}, \ldots, a_{n}$ tame if it satisfies
$$
1 \cdot a_{1} \leq 2 \cdot a_{2} \leq \ldots \leq n \cdot a_{n}
$$
Determine the number of tame permutations of $1,2, \ldots, n$.
$$
1 \cdot a_{1} \leq 2 \cdot a_{2} \leq \ldots \leq n \cdot a_{n}
$$
Determine the number of tame permutations of $1,2, \ldots, n$.