Number Magic

Question :
What is a 'Sub-Factorial' ?

Answer :
To find the sub-factorial of an integer, supposing 'n' is the integer the sub-factorial of
n = n! x ((1/2)! - (1/3)! + (1/4)! . . . ((-1)n) / n!)
For example the sub-factorial of 4 :

= 4! ((1/2)! - (1/3)! + (1/4)!)

= 24 ((1/2) - (1/6) + (1/24))

= 9
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