\quad (2n-1)!! = \frac{(2n)!}{2^n n!} \\

\Leftrightarrow 2^n n! = \frac{(2n)!}{(2n-1)!!} \\

\Leftrightarrow 2^n n! = 2n(2n-2) \cdots 2 \\

\Leftrightarrow n! = \frac{2n}{2} \cdot \frac{2n-2}{2} \cdots \frac{2}{2} \\

\Leftrightarrow n! = n(n-1)\cdots 1