factorial
    adj 1: of or relating to factorials
    n 1: the product of all the integers up to and including a given
         integer; "1, 2, 6, 24, and 120 are factorials"

Factorial \Fac*to"ri*al\, a.
   1. Of or pertaining to a factory. --Buchanan.
      [1913 Webster]

   2. (Math.) Related to factorials.
      [1913 Webster]

Factorial \Fac*to"ri*al\, n. (Math.)
      (a) pl. A name given to the factors of a continued product
          when the former are derivable from one and the same
          function F(x) by successively imparting a constant
          increment or decrement h to the independent variable.
          Thus the product F(x).F(x + h).F(x + 2h) . . . F[x +
          (n-1)h] is called a factorial term, and its several
          factors take the name of factorials. --Brande & C.
      (b) The product of the consecutive whole numbers from
          unity up to any given number; thus, 5 factorial is the
          product of 5 times four times three times two times
          one, or 120.
          [1913 Webster +PJC]

factorial

    The mathematical function that takes a
   natural number, N, and returns the product of N and all
   smaller positive integers.  This is written

   	N! = N * (N-1) * (N-2) * ... * 1.

   The factorial of zero is one because it is an empty
   product.

   Factorial can be defined recursively as

   	0! = 1
   	N! = N * (N-1)!		, N > 0

   The gamma function is the equivalent for real numbers.

   For example, the number of ways of shuffling 52 playing cards is
   52! or nearly 10^68.  <52 Factorial>.

   (2012-11-23)