Question 109
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
$$
a_{1} \leqslant 2 a_{2} \leqslant 3 a_{3} \leqslant \ldots \leqslant n a_{n}
$$
$$
a_{1} \leqslant 2 a_{2} \leqslant 3 a_{3} \leqslant \ldots \leqslant n a_{n}
$$