Definition:Factorial/Historical Note

Definition
The symbol $!$ used on for the factorial, which is now universal, was introduced by  in his $1808$ work.

Before that, various symbols were used whose existence is now of less importance.

Notations for $n!$ in history include the following:
 * $\left[{n}\right]$ as used by
 * $\mathop{\Pi} n$ as used by
 * $\left\lvert{\kern-1pt\underline n}\right.$ and $\left.{\underline n\kern-1pt}\right\rvert$, once popular in England and Italy.

declared his reservations about 's notation thus:
 * Amongst the worst barbarisms is that of introducing symbols which are quite new in mathematical, but perfectly understood in common, language. Writers have borrowed from the Germans the abbreviation $n!$ ... which gives their pages the appearance of expressing admiration that $2$, $3$, $4$, etc., should be found in mathematical results.

The use of $n!$ for non-integer $n$ is uncommon, as the Gamma function tends to be used instead.