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The factorial of a given natural number n is the product of all the natural numbers less than or equal to n. The factorial of n is denoted usually by n! Thus,
n! = 1 × 2 × ... × n
For large n an approximate expression for n! is given by Stirling’s formula. The number of permutations of n things taken all at a time is the factorial of n.
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.