Hi. This is my first attempt to create a fast growing notation.
In all examples a,b,c,d,... are natural numbers.
First, {a} = a+1.
Then, {a,1} = {a}
Finally, {a,b} = {...{{{a,b-1},b-1},b-1}...} with a layers of nesting.
I believe that this reaches in FGH.
The next extension of this is LFAN.