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Is there a relationship between n! and !n?

 Yes.

 

Oh, you want more. Right, then:

and (even cooler [if that's possible!]!)


 


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Sum-thing else

In addition to the recursion formulas shown, a subfactorial  can be developed using a summation. As an example, we'll develop the result for !4 , which we have addressed in an earlier post. ...which is the same answer we developed using the recursion  approach.