Do you know everything about Factorials?

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When I was in 7th grade at Amity Junior High School in Orange Connecticut, I gave a presentation on Factorial numbers.

Here’s some interesting code:

FOR i = 1 TO 80

      ?i,Factorial(i),SQRT(2*PI()*i)*(i/EXP(1))^i

ENDFOR

PROCEDURE Factorial(n)

      IF n=1

            RETURN n

      ENDIF

RETURN n*Factorial(n-1)

     

What do the base of natural logs (exp(1) = 2.718281828…), PI (3.14159…) and the square root of 2 have to do with Factorial ?

(In case you were wondering, I did not include the transcendental math in my 7th grade presentation)

I don’t know everything about the fascinating Factorials!