# Factorial

## Definition

Let  be a nonnegative integer. The factorial of , denoted , and read as n factorial, is defined as the product of all the natural numbers from  to . Note that  is defined as .

 is also the order of the symmetric group, or the group of all permutations, on a set of size .

## Behavior

The ID of the sequence in the Online Encyclopedia of Integer Sequences is A000142

### Initial values

Here are the values of  for small : .