double factorial

The double factorialMathworldPlanetmath of a positive integer n is the product n!! of the positive integers less than or equal to n that have the same parity as n, that is,


where kn denotes 1 if n is an odd numberMathworldPlanetmathPlanetmath and 2 if n is an even number.

For example,


Note that n!! is not the same as (n!)!.

Observe that (2n)!!=2nn! and (2n+1)!!=(2n+1)!2nn!.

Title double factorial
Canonical name DoubleFactorial
Date of creation 2013-03-22 12:24:54
Last modified on 2013-03-22 12:24:54
Owner drini (3)
Last modified by drini (3)
Numerical id 9
Author drini (3)
Entry type Definition
Classification msc 05A10