User blog comment:Alejandro Magno/Extended Arrow Notation/@comment-172.56.14.221-20150306044057/@comment-99.185.0.100-20150808170435

I think ^^(n)^^ becomes:

^(n)^ when n=1

(^(n)^)(n)(^(n)^) when n=2

((^(n)^)(n)(^(n)^))(n)((^(n)^)(n)(^(n)^)) when n=3

...

As for how far ^{n}^ is in array space, probably less than legions.

* Tetrational arrays, the largest well-defined part of BEAF, match up with ^((^(n)^)(n)(^(n)^))^