Factorial of odds I am trying to find a simple factorial of all the preceding odd numbers. If $9$ were to be picked the equation would read $9\times 7\times 5\times 3\times 1$ (only odd numbers can be picked). Would the following fraction work?


$$\dfrac{x!}{2^{\left(\frac{x-1}{2}\right)}\left(\frac{x-1}{2}\right)!}$$



Hint:
\begin{align}
9\cdot7\cdot5\cdot3\cdot1&= \frac{9\cdot8\cdot7\cdot6 \cdot5\cdot4\cdot3\cdot2\cdot1}{8\cdot6\cdot4\cdot2}\\&= \frac{9\cdot8\cdot7\cdot6 \cdot5\cdot4\cdot3\cdot2\cdot1}{2^4(4\cdot3\cdot2\cdot1)}\end{align}
