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In mathematics, the factorial of a non-negative integer, denoted by !, is the product of all positive integers less than or equal to . The factorial of also equals ...
These are counted by the double factorial 15 = (6 − 1)‼. In mathematics, the double factorial of a number n, denoted by n‼, is the product of all the positive integers up to n that have the same parity (odd or even) as n. [1] That is,
The term "factorial number system" is used by Knuth, [3] while the French equivalent "numération factorielle" was first used in 1888. [4] The term "factoradic", which is a portmanteau of factorial and mixed radix, appears to be of more recent date. [5]
(n factorial) is the number of n-permutations; !n (n subfactorial) is the number of derangements – n-permutations where all of the n elements change their initial places. In combinatorial mathematics , a derangement is a permutation of the elements of a set in which no element appears in its original position.
In mathematics, the falling factorial (sometimes called the descending factorial, [1] falling sequential product, ... [5] In the theory of special functions ...
Comparison of Stirling's approximation with the factorial. In mathematics, Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials. It is a good approximation, leading to accurate results even for small values of .
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2.4 Modified-factorial denominators. 2.5 Binomial coefficients. 2.6 Harmonic numbers. ... Series (mathematics) List of integrals; Summation § Identities; Taylor series;