Double factorial
![The fifteen different chord diagrams on six points or equivalently the fifteen different perfect matchings on a six-vertex complete graph](/Images/godic/202501/09/Chord_diagrams_K6_matchings.svg0406.png")
![The fifteen different rooted binary trees (with unordered children) on a set of four labeled leaves](/Images/godic/202501/09/Unordered_binary_trees_with_4_leaves.svg0406.png")
In mathematics, the product of all the integers from 1 up to some non-negative integer n that have the same parity as n is called the double factorial or semifactorial of n and is denoted by n!!. That is,
where ![m=\lceil n/2 \rceil - 1.](/Images/godic/202501/09/fe0f1b1eb4487f206309fb294d290dc20406.png")
A consequence of this definition is that (as an empty product)