The falling factorial \((x)_n\) is defined as \(x \cdot (x - 1) \cdot (x - 2) \cdot \ldots \cdot (x - (n - 1))\).[1]

Examples

\((x)_0\) = 1
\((x)_1\) = x
\((x)_2\) = x(x-1)
\((n)_n\)=n!

Sources

See also

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: · Superfactorial by Sloane and Plouffe · Torian · Factorexation · Mixed factorial · Bouncing Factorial
Community content is available under CC-BY-SA unless otherwise noted.