User blog comment:King2218/Extended Factorial Notation/@comment-10429372-20140209182927

Hello King2218, welcome to the wiki. Your notation is quite good, although it is much like hyperfactorial array notation and nested factorial notation. I'm wondering about your definition of arrays.

Your notation is a bit unclear. Does 3!!!! expand like this?:

$$((3\uparrow^32\uparrow^31)\uparrow^2(2\uparrow^31)\uparrow^21)^{((2\uparrow^31)\uparrow^21)^1*((2\uparrow^31)\uparrow^21)^1*1$$

Here is a formal definition for n!!:

1!!=1

n!!=n(n-1)!!*(n-1)!!