1, any factorial representation of natural numbers greater than 1 n: n! = 1× 2× 3× …× n or n! =n×(n- 1)！

2. Double factorial of n: When n is an odd number, it means the product of all odd numbers not greater than n. ..

Such as: 7! = 1×3×5×7

3. When n is an even number, it means the product of all even numbers not greater than n (except 0).

Such as: 8! =2×4×6×8

4. factorial representation of integer n less than 0:

(-n)！ = 1 / (n+ 1)！

Factors of 5 and 0: 0! =0

6. Combination number formula

Extended data:

Factorial factor is an operation symbol invented by Keyston Kramp (1760–1826) in 1808. Factorial factor is also a term in mathematics. Factorial factor refers to the required number obtained by multiplying 1 by 2 times 3 times 4.

In addition, mathematicians define 0! = 1, so 0! = 1! Usually, the factorial is defined in the range of natural numbers, and there is no factorial for decimals, like 0.5! ,0.65! ,0.777! It's all wrong

But sometimes we define the Gamma function as the factorial of non-integers, because when x is a positive integer n, the value of the Gamma function is the factorial of n- 1

References:

Baidu encyclopedia-factorial