User blog:DerivedSugar177/Star Factorial

Star Factorial
A new type of factorial that is defined as <*n*> or S(n)!

Rules :

1) S(0)! = 0

2) S(1)! = 1

3) S(n)! = n^^^^....( n ^'s )....^^^^n^^^^....( n ^'s )....^^^^n^^^^^....   ( repeat n times )

Examples : 

'''S(0)! = 0'''

'''S(1)! = '''1

'''S(2)! = '''2^^2 = 4

'''S(3)! = 3^^^3^^^3 = 3^^^(3^3^3^3^3.....(3^^3 3's).....3^3^3^3^3) = 3^^3^^3^^3^^3.....3^^3  ( 3^^^3 3^^3's )'''

'''S(10)! = '''10^^^^^^^^^^10^^^^^^^^^^10^^^^^^^^^^10^^^^^^^^^^10^^^^^^^^^^10^^^^^^^^^^10^^^^^^^^^^10^^^^^^^^^^10^^^^^^^^^^10

We extend this to S(n)!!

'''S(0)!! = '''0

'''S(1)!! = '''1

'''S(2)!! = '''2^^^^2^^^^2^^^^2

'''S(3)!! = '''3^^^^^^....(S(3)! ^'s)....^^^^^^3^^^^^^....(S(3)! ^'s)....^^^^^^3...... ( repeat S(3)! times )

This gives us that

S(0)# = 0    ( # : rest of the array )

S(1)# = 1

S(2)# = 2^^^^^^...( S(2)#-1 ^'s ''')...^^^^^^2^^^^^^...... ( repeat S(2)#-1 times )'''