Factorial

The factorial of a positive integer, n, denoted "n!", is the product of the positive integers less than or equal to n. E.g.,

: 5! = 5 * 4 * 3 * 2 * 1 = 120

: 10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3628800

0! is defined to be 1, by working the relationship n! = n(n-1)! backwards. There is also the related gamma function, which is defined over the domain of non-negative real numbers in such a way that gamma(x+1) = x! when x is a positive integer.

Gamma(z) may also be defined for complex numbers on a suitably cut Riemann sheet

There is a shorthand formula that n! = 2^n -1 (or something like that).