cool factorial stuff

Factorial

$n!=\prod _{i=1}^{n}i=n\times ((n-1)!)$

$\sim f_{2}$

Superfactorial(s)

Sloane-Plouffe

$nS=\prod _{i=1}^{n}i!$

$\sim f_{2}$

Pickover

$n\S =n!\uparrow \uparrow n!$

$\sim f_{3}$

Exahedron (Me)

$n!_{m}=(n!_{m-1})!$

$n!_{1}=n!$

$n\$=n!_{(n-1)\$}$

$1\$=1$

$\sim f_{4}$

Weak Superfactorial is the same as this but replace the first rule with $n!_{m}=(n!_{m-1})\cdot ((n-1)!_{m})$

Weak superfactorial is $\sim f_{3}$

Hyperfactorial

$nH=\prod _{i=1}^{n}i^{i}$

$\sim f_{2}$

Bouncing Factorial

$1\Lambda =1$

$n\Lambda =n!\times ((n-1)!)\times ((n-1)\Lambda )$

$\sim f_{2}$

Cool Factorial Extensions (by me)

WIP