2020 IMO Shortlist C1

Let $n$ be a positive integer. Find the number of permutations $a_{1}, a_{2}, \ldots, a_{n}$ of the sequence $1,2, \ldots, n$ satisfying $$a_{1} \leq 2 a_{2} \leq 3 a_{3} \leq \ldots \leq n a_{n}$$ (United Kingdom)

令 $n$ 为正整数。求序列 $1,2, \ldots, n$ 满足 $$a_{1} \leq 2 a_{2} \leq 3 a_{3} \leq \ldots \leq n a_{n}$$ 的排列数 $a_{1}, a_{2}, \ldots, a_{n}$ (英国)