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# Multifactorial number

## Definition

A Factorial number is defined by the product

$\displaystyle{ n! = 1 \cdot 2 \cdot 3 \cdots (n{-}2) \cdot (n{-}1) \cdot n }$

for $\displaystyle{ n &ge; 1 }$.

A Multifactorial number is denoted by

$\displaystyle{ n!! = (n) \cdot (n-2) \cdot (n-4) \cdots }$
$\displaystyle{ n!!! = (n) \cdot (n-3) \cdot (n-6) \cdots }$

and so on.

To clarify and make reading easier $\displaystyle{ n!!!!! }$ is displayed as $\displaystyle{ n!_5 }$.