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n ! {\displaystyle n!} 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 the product of with the next smaller factorial: For example, The value of 0! is 1, according to the convention for an empty product.
Definition. The factorial number system is a mixed radix numeral system: the i -th digit from the right has base i, which means that the digit must be strictly less than i, and that (taking into account the bases of the less significant digits) its value is to be multiplied by (i − 1)! (its place value). Radix/Base. 8.
In combinatorial mathematics, a derangement is a permutation of the elements of a set in which no element appears in its original position. In other words, a derangement is a permutation that has no fixed points. 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 ...
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 . It is named after James Stirling, though a related but less precise result was first stated ...
Factorion. 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. [ 4]
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, Restated, this says that for even n, the double factorial 2 is while for odd n it is For example, 9‼ = 9 × 7 × 5 × 3 × 1 = 945. The zero double factorial 0‼ ...