Factorial

Definition

Let $n$ be a nonnegative integer. The factorial of $n$, denoted $n!$, and read as n factorial, is defined as the product of all the natural numbers from $1$ to $n$. Note that $0!$ is defined as $1$.

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

Behavior

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

Initial values

Here are the values of $n!$ for small $n=0,1,2,3,4,5,6,7$: $1,1,2,6,24,120,720,5040$.

Related notions

• lcm of all numbers so far: This is the exponential of the second Chebyshev function and also equals the exponent of the symmetric group of degree $n$.
• Maximum product over additive partitions
• Maximum lcm over additive partitions
• Primorial is the product of the first few primes.