Factorial fun!

Number Theory Level 2

Suppose that $n!!$ is defined as follows:

$n!! = \begin{cases} n \times (n-2) \times \cdots \times 5 \times 3 \times 1 &\text{if } n \text{ is odd}; \\ n \times (n-2) \times \cdots \times 6 \times 4 \times 2 &\text{if } n \text{ is even}; \\ 1 &\text{if } n = 0, - 1. \\ \end{cases}$