Double factorial

The fifteen different chord diagrams on six points or equivalently the fifteen different perfect matchings on a six-vertex complete graph

The fifteen different rooted binary trees (with unordered children) on a set of four labeled leaves

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 $m=\lceil n/2 \rceil - 1.$ A consequence of this definition is that (as an empty product)

单词	Double factorial
释义	Double factorial 英语百科 Double factorial 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 $m=\lceil n/2 \rceil - 1.$ A consequence of this definition is that (as an empty product)
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