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The factorial of also equals the product of with the next smaller factorial: ! = () = ()! For example, ! =! = = The value of 0! is 1, according to the convention for an empty product . [ 1 ]
From this it follows that the rightmost digit is always 0, the second can be 0 or 1, the third 0, 1 or 2, and so on (sequence A124252 in the OEIS).The factorial number system is sometimes defined with the 0! place omitted because it is always zero (sequence A007623 in the OEIS).
This experiment is an example of a 2 2 (or 2×2) factorial experiment, so named because it considers two levels (the base) for each of two factors (the power or superscript), or #levels #factors, producing 2 2 =4 factorial points. Cube plot for factorial design . Designs can involve many independent variables.
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.
The value of each is taken to be 1 (an empty product) when =. These symbols are collectively called factorial powers. [2] The Pochhammer symbol, introduced by Leo August Pochhammer, is the notation (), where n is a non-negative integer.
2.3 Trigonometric, inverse trigonometric, hyperbolic, and inverse hyperbolic functions relationship 2.4 Modified-factorial denominators 2.5 Binomial coefficients
In number theory, a factorion in a given number base is a natural number that equals the sum of the factorials of its digits. [ 1 ] [ 2 ] [ 3 ] The name factorion was coined by the author Clifford A. Pickover .
Stirling permutations, permutations of the multiset of numbers 1, 1, 2, 2, ..., k, k in which each pair of equal numbers is separated only by larger numbers, where k = n + 1 / 2 . The two copies of k must be adjacent; removing them from the permutation leaves a permutation in which the maximum element is k − 1 , with n positions into ...