**Factorial
**

The *factorial* of a non-negataive integer *n*, designated *n*!, can be
defined recursively as

0! = 1

*n*! =* n*(*n* – 1)! for *n* > 0.

Intuitively, for a positive integer *n*, *n*! is the product of positive
integers up to and including *n*.

Sometimes it's more useful to think of *n*! as the product of positive
integers from *n* down to 1. That viewpoint, for example, makes clear the
relationship

*n*! = *n*(*n* – 1)!

Factorials are used in counting numbers of permutations and combinations.

The gamma function is defined for all real numbers, but outputs factorial values for non-negative integer input. Information about the gamma function can be found in advanced calculus texts.

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