Recurrence Relation $F(n) = (n-1)F(n-2)$

Question

How can I solve the following recurrence relation in terms of $f(1)$ ? -Assuming $n$ is odd.
$$F(n) = (n-1)\cdot F(n-2)$$

Answer 1

Welcome to math Stack Exchange! Divide $F_n$ by $F_{n-2}$ and multiply lower terms for the product

$$F_n = \frac{F_n}{F_{n-2}}\frac{F_{n-2}}{F_{n-4}}\cdots\frac{F_3}{F_1} F_1 = (n-1)(n-3)\cdots 2\ F_1$$