# Multifactorial

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The multifactorial is a generalization of the double factorial,[1] defining:

• $$n!! = n \cdot(n - 2) \cdot(n - 4) \cdot(n - 6)\ldots$$
• $$n!!! = n \cdot(n - 3) \cdot(n - 6) \cdot(n - 9)\ldots$$
• $$n!!!! = n \cdot(n - 4) \cdot(n - 8) \cdot(n - 12)\ldots$$

and so forth. For example, 10!!! = 10 · 7 · 4 · 1 = 280.

It is important to note that multifactorials should not be interpreted as nested factorials, e.g. $$n!! < (n!)!$$ and $$n!!! < ((n!)!)!$$.[2] Multifactorials actually grow slower than normal factorials, so much slower than iterated factorials.

1. [1]
2. [2]