noun

• (mathematics, combinatorics) The result of multiplying a given number of consecutive integers from 1 to the given number. In equations, it is symbolized by an exclamation mark (!). For example, 5! = 1 × 2 × 3 × 4 × 5 = 120.
  "The expression #123;#125;#95;nC#95;r means the number of combinations of n things taken r at a time. It is also written #92;binomnr, and is equal to#92;frac#123;n(n-1)(n-2)(n-3)#92;cdots#92;cdots(n-r#43;1)#125;#123;r#33;#125;or n#33;#47;r#33;(n-r)#33;, in which r#33; is read "factorial r" and denotes the product of all the integral numbers from 1 to r inclusive."

adj

• (mathematics) Of or pertaining to a factor or factorial.
  "I shall denote, as usual, the factorial product of the numbers up to n by n#33;, but I have found it necessary to introduce a separate notation for the products of successive even or odd numbers. I consequently definen#33;#33;#61;n#92;cdot(n-2)#33;#33;.Starting with1#33;#33;#61;1,#92;quad 2#33;#33;#61;2,it follows that, for positive values of n,n#33;#33;#61;n#92;cdotn-2#92;cdotn-4#92;cdots,where the last factor is either 1 or 2, according as n is odd or even."
• (dated) Of or pertaining to a factory.