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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.

Sources Edit

  1. [1]
  2. [2]

See also Edit

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
Tetrational growth: Exponential factorial · Expostfacto function · Superfactorial by Clifford Pickover
Array-based extensions: Hyperfactorial array notation · Nested factorial notation
Other googological variants: · Superfactorial by Sloane and Plouffe · Torian · Factorexation · Mixed factorial

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