User blog:Alejandro Magno/Make an extension of the notation remake 2

Reviving my old post.

NOTE: This notation was coined by me to start off.

Rules:

1. Do not invent new notations.

2. No cheating!

3. Define your notations well.

4. ...that's all?

I will start with:

a[n] = a^(n)^a

a[n,m] = a[a[a[...[a,m-1]...],m-1],m-1] with n levels

a[n,1] = a[n] and a[#,1] = a[#]

a[...,n,m] = a[[[...[...,a,m-1]...]...,a,m-1]...,a,m-1] with n levels

etc.