Pentation? How quaint. For other Large Number fans, David Metzler has a wonderful playlist that goes way down the rabbit hole of the fast growing hierarchy:
https://www.youtube.com/playlist?list=PL3A50BB9C34AB36B3
Highly recommended.
Almost all of these mind-bogglingly large numbers are built around recursion, like the Ackermann function, which effectively has an argument for the number of Knuth up arrows to use. Then you can start thinking about feeding the Ackermann function into that slot and enjoy the sense of vertigo at how insane that becomes.
I find it fascinating how quickly the machinery of specifying large numbers probes the limits of what's definable within the mathematical systems we use.
You might already know this, but the busy beaver function grows faster than any computable function. So although the best known lower bound of BB(6) can be expressed with just pentation, generally speaking the BB function is certainly beyond any standard operation in terms of fast growth
I got one recently due to some persistent wrist issues I've been having because it is the first ergo mouse I've had that ticks every box for me. It's not flawless but I still strongly recommend considering it if you're looking for something in this category.
The designer previously posted about it on HN here: https://news.ycombinator.com/item?id=35613630