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2. Falling and rising factorials - Wikipedia

   en.wikipedia.org/wiki/Falling_and_rising_factorials

   In this article, the symbol () is used to represent the falling factorial, and the symbol () is used for the rising factorial. These conventions are used in combinatorics , [ 4 ] although Knuth 's underline and overline notations x n _ {\displaystyle x^{\underline {n}}} and x n ¯ {\displaystyle x^{\overline {n}}} are increasingly popular.

3. Multiple factor analysis - Wikipedia

   en.wikipedia.org/wiki/Multiple_factor_analysis

   Multiple factor analysis (MFA) is a factorial method [1] devoted to the study of tables in which a group of individuals is described by a set of variables (quantitative and / or qualitative) structured in groups.

4. Stirling's approximation - Wikipedia

   en.wikipedia.org/wiki/Stirling's_approximation

   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 .

5. Factorial - Wikipedia

   en.wikipedia.org/wiki/Factorial

   Here () denotes the sum of the base-digits of , and the exponent given by this formula can also be interpreted in advanced mathematics as the p-adic valuation of the factorial. [54] Applying Legendre's formula to the product formula for binomial coefficients produces Kummer's theorem , a similar result on the exponent of each prime in the ...

6. Derangement - Wikipedia

   en.wikipedia.org/wiki/Derangement

   (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.

7. Double factorial - Wikipedia

   en.wikipedia.org/wiki/Double_factorial

   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, n ! ! = ∏ k = 0 ⌈ n 2 ⌉ − 1 ( n − 2 k ) = n ( n − 2 ) ( n − 4 ) ⋯ . {\displaystyle n!!=\prod _{k=0}^{\left\lceil {\frac {n}{2}}\right\rceil -1}(n-2k ...