An improved version of Googolological notation
Two entry arrays[]
First if all {a,b} is equal to a^^^b.
Multi-entry arrays[]
Multi-entry arrays are solved recursively: {...,a,b} = {{...,a},b}.
Square brackets[]
[a,b] is equal to {a,a,...,a,a} with b a's
Square brackets can also be multi-entry arrays. Solve them like normal arrays
Higher levels[]
[...] becomes {...}2.
Then we define {...}3, it is to [...] as [...] is to {...}.
The f function[]
f(n) = {n,n}n.