The multifactorial is a generalization of the double factorial, 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 $$n!!! < ((n!)!)!$$. Multifactorials actually grow slower than normal factorials, so much slower than nested factorials.

## Sources

Main article: Factorial
Multifactorials: Double factorial · Multifactorial
Falling and rising: Falling factorial · Rising factorial
Other mathematical variants: Alternating factorial · Hyperfactorial · q-factorial · Roman factorial · Subfactorial · Weak factorial · Primorial · Compositorial · Semiprimorial
Tetrational growth: Exponential factorial · Expostfacto function · Superfactorial by Clifford Pickover
Nested Factorials: Tetorial · Petorial · Ectorial · Zettorial · Yottorial
Array-based extensions: Hyperfactorial array notation · Nested factorial notation
Other googological variants: · Tetrofactorial · Superfactorial by Sloane and Plouffe · Torian · Factorexation · Mixed factorial · Bouncing Factorial