factorial

in mathematics, a factorial of a number $n$ is $n!$ and is defined for a positive integer $n$ as $n!=n(n-1)(n-2)\dots (2)(1)$
for example, $4!=4\cdot 3\cdot 2\cdot 1=24$

the special case $0!$ is defined as $0!=1$, consistent with the interpretation that there is a single permutation of zero elements, the empty set.

the triangular number $T_n$ can be regarded as the additive analog of the factorial $n!$

guide to factorials