Questions on the factorial function, $n!=n\cdot(n-1)\cdot...\cdot1$. Consider using the tag (gamma-function) if dealing with noninteger arguments.
The factorial is defined as the product of all positive integers less than or equal to some integer $n$, written $n!$.
For example:
$$10!=10\cdot 9\cdot 8\cdot...\cdot 2\cdot 1$$
Multiple $!$'s skip integers ($!!$ skip $2$, $!!!$ skip $3$, etc..), so for example: $$10!!!=10\cdot7\cdot4\cdot1$$
This function is only defined over non-negative integers, in particular $0!=1$.
The gamma-function extends it to all complex numbers that are not non-positive integers. In particular, we have that:
$$n!=\Gamma(n-1)$$
