Difference between revisions of "Factorial"

From Number
Jump to: navigation, search
(Related notions)
 
(One intermediate revision by the same user not shown)
Line 9: Line 9:
 
===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"/>
 
+
  
 
==Related notions==
 
==Related notions==
Line 16: Line 15:
 
* [[lcm of all numbers so far]]: This is the exponential of the [[second Chebyshev function]] and ''also'' equals the [[groupprops:exponent of a group|exponent]] of the symmetric group of degree <math>n</math>.
 
* [[lcm of all numbers so far]]: This is the exponential of the [[second Chebyshev function]] and ''also'' equals the [[groupprops:exponent of a group|exponent]] of the symmetric group of degree <math>n</math>.
 
* [[Maximum product over additive partitions]]
 
* [[Maximum product over additive partitions]]
* [[Maximum lcm over additive partitions]]
+
* [[Landau's function]] is the maximum lcm over additive partitions.
 
* [[Primorial]] is the product of the first few primes.
 
* [[Primorial]] is the product of the first few primes.

Latest revision as of 17:58, 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