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  2. Factorial - Wikipedia

    en.wikipedia.org/wiki/Factorial

    2: 2 3: 6 4: 24 5: 120 6: 720 ... Stirling's approximation provides an accurate approximation to the factorial of large numbers, ... a 1975 calculator with a ...

  3. Double factorial - Wikipedia

    en.wikipedia.org/wiki/Double_factorial

    Unrooted binary trees with ⁠ n + 5 / 2 ⁠ labeled leaves. Each such tree may be formed from a tree with one fewer leaf, by subdividing one of the n tree edges and making the new vertex be the parent of a new leaf. Rooted binary trees with ⁠ n + 3 / 2 ⁠ labeled leaves. This case is similar to the unrooted case, but the number of edges ...

  4. Factorion - Wikipedia

    en.wikipedia.org/wiki/Factorion

    There are finitely many natural numbers less than , so the number is guaranteed to reach a periodic point or a fixed point less than , making it a preperiodic point. For b = 2 {\displaystyle b=2} , the number of digits k ≤ n {\displaystyle k\leq n} for any number, once again, making it a preperiodic point.

  5. Derangement - Wikipedia

    en.wikipedia.org/wiki/Derangement

    The number of derangements of a set of size n is known as the subfactorial of n or the n th derangement number or n th de Montmort number (after Pierre Remond de Montmort). Notations for subfactorials in common use include !n, D n, d n, or n¡ . [a] [1] [2] For n > 0 , the subfactorial !n equals the nearest integer to n!/e, where n!

  6. Glossary of mathematical symbols - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_mathematical...

    1. Factorial: if n is a positive integer, n! is the product of the first n positive integers, and is read as "n factorial". 2. Double factorial: if n is a positive integer, n!! is the product of all positive integers up to n with the same parity as n, and is read as "the double factorial of n". 3.

  7. Factorial number system - Wikipedia

    en.wikipedia.org/wiki/Factorial_number_system

    The number 2982 is 4:0:4:1:0:0:0! in factoradic, and that number picks out digits (4,0,6,2,1,3,5) in turn, via indexing a dwindling ordered set of digits and picking out each digit from the set at each turn:

  8. Factorization - Wikipedia

    en.wikipedia.org/wiki/Factorization

    For example, 3 × 5 is an integer factorization of 15, and (x – 2)(x + 2) is a polynomial factorization of x 24. Factorization is not usually considered meaningful within number systems possessing division , such as the real or complex numbers , since any x {\displaystyle x} can be trivially written as ( x y ) × ( 1 / y ) {\displaystyle ...

  9. Kempner function - Wikipedia

    en.wikipedia.org/wiki/Kempner_function

    In number theory, the Kempner function [1] is defined for a given positive integer to be the smallest number such that divides the factorial!. For example, the number 8 {\displaystyle 8} does not divide 1 ! {\displaystyle 1!} , 2 ! {\displaystyle 2!} , or 3 ! {\displaystyle 3!} , but does divide 4 ! {\displaystyle 4!} , so S ( 8 ) = 4 ...