Multifactorial number

Definition

A Factorial number is defined by the product

[math]\displaystyle{ n! = 1 \cdot 2 \cdot 3 \cdots (n{-}2) \cdot (n{-}1) \cdot n }[/math]

for [math]\displaystyle{ n \geq 1 }[/math].

A Multifactorial number is denoted by

[math]\displaystyle{ n!! = (n) \cdot (n-2) \cdot (n-4) \cdots }[/math]

[math]\displaystyle{ n!!! = (n) \cdot (n-3) \cdot (n-6) \cdots }[/math]

and so on.

To clarify and make reading easier [math]\displaystyle{ n!!!!! }[/math] is displayed as [math]\displaystyle{ n!_5 }[/math].