Whose factorial is from 1 to whom, as simple as that.
(2n)！ = 1×2×3×2n
With "m! ! "Express delivery.
When m is a natural number, it means the product of all positive integers not exceeding m and having the same parity with m, such as:
Example:
3! ! = 1*3=3
5! ! = 1*3*5= 15
6! ! =2*4*6=48
8! ! =2*4*6*8=384
Another 0! ! = 1! ! = 1
When m is a negative odd number, it means the reciprocal of the absolute product of all negative odd numbers whose absolute values do not exceed their absolute values. For example:
Example:
(-5)! ! = 1/(|- 1| * |-3| * |-5|)= 1/ 15
(-7)! ! = 1/(|- 1| * |-3| * |-5| * |-7|)= 1/ 105
(-9)! ! = 1/(|- 1| * |-3| * |-5| * |-7| * |-9|)= 1/945
The other one (-1)! ! = 1
When m is a negative even number, m! ! Does not exist.
Conversion between second order and first order;
Important equation: (2n- 1)! ! (2n)！ ! =[ 1×3×…×(2n- 1)][2×4×…×(2n)]=(2n)！