# Difference between revisions of "Factorial"

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===Initial values=== | ===Initial values=== | ||

− | The initial values of <math>k!</math> for <math>k=0,1,2,3,4,\dots</math> are given as: <section begin="list"/>[[1]], [[2]], [[6]], [[24]], [[120]], [[720]], [[5040]], [[40320]], [[362880]] [[Oeis:A000142|View list on OEIS]]<section end="list"/> | + | The initial values of <math>k!</math> for <math>k=0,1,2,3,4,\dots</math> are given as: <section begin="list"/>[[1]], [[2]], [[6]], [[24]], [[120]], [[720]], [[5040]], [[40320]], [[362880]], <toggledisplay>3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000</toggledisplay> [[Oeis:A000142|View list on OEIS]]<section end="list"/> |

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==Related notions== | ==Related notions== |

## Revision as of 17:52, 3 July 2012

## 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

### Initial values

The initial values of for are given as: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, [SHOW MORE] View list on OEIS## 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 . - Maximum product over additive partitions
- Maximum lcm over additive partitions
- Primorial is the product of the first few primes.