Double factorial

Double factorial is a method of calculating how many times a number is repeated in a geometric equation. This way, we can calculate the number of times a product is used in its life-time.

The double factorial of n is written as [math]\displaystyle{ n!! }[/math]. When n is a positive odd integer, [math]\displaystyle{ n!! }[/math] is defined as [math]\displaystyle{ n \cdot (n-2) \cdot\, \cdots \, \cdot 3 \cdot 1 }[/math]. When n is an positive even integer, [math]\displaystyle{ n!! }[/math] is defined as [math]\displaystyle{ n \cdot (n-2) \cdot\, \cdots \, \cdot 4 \cdot 2 }[/math]. By definition, [math]\displaystyle{ 0!! = 1 }[/math].

Double Factorial Media

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  The fifteen different chord diagrams on six points, or equivalently the fifteen different perfect matchings on a six-vertex complete graph. These are counted by the double factorial 15 = (6 − 1)‼.

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  The fifteen different rooted binary trees (with unordered children) on a set of four labeled leaves, illustrating 15 = (2 × 4 − 3)‼ (see article text).

Related pages

• Factorial
• Permutation