TITLE: Why is the double factorial $(-1)!! = 1$, by definition?
QUESTION [9 upvotes]: By definition, the double factorial $(-1)!! = 1$. How can this be rationalized?

REPLY [4 votes]: One answer is to maintain that
$$
n!!=\frac{(n+2)!!}{n+2}
$$
for all $n$.  In this case, we must have
$$
(-1)!!=\frac{(-1+2)!!}{(-1+2)}=\frac{1!!}{1}=1.
$$