## FANDOM

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In January 25th 2016 I was editing the article about superfactorial, I made a few corrections and added some values for $$n\$$ as defined by Clifford Pickover.

I was reading about the two different definitions of superfactorial in the article, then I realized what would be a third definition for $$n\$$, so I decided to create a new factorial-based function.

My inttention was to create a nice new $$n\$$ function that grew faster than that defined by Sloane & Plouffeand that does not involve tetration, as observed in $$n\$$ reported by Clifford Pickover.

Considering the product of factorials as in $$n\$$ reported by Sloane & Plouffe, after some attempts, I got through a new definition for $$n\$$ as follows:

$$n\ = (\underbrace{11...11}_{n}n)\times((\underbrace{11...11}_{n-1}n)!)\times((\underbrace{11...11}_{n-2}n)!^{2})\cdots((111n)!^{(n-3)})\times((11n)!^{(n-2)})\times(n!^{(n-1)})$$

where $$!^{2}$$, $$!^{(n-3)}$$, $$!^{(n-2)}$$ and $$!^{(n-1)}$$ are from Nested factorial notation as defined by Aarex Tiaokhiao.

The first six superfactorials as described here are:

$$1\ = 1$$

$$2\ = 44$$

$$3\ = 2.08191223228633...\times10^{42} = 2pt1.62652987982134...$$

$$4\ = 10^{10^{56.15691512713508...}} = 2pt56.15691512713508... = 3pt1.74940324263919...$$

$$5\ = 4pt2.44662641649391...$$

$$6\ = 5pt3.24295297233703...$$