User blog comment:Deedlit11/A rigorous definition for pentational arrays/@comment-5150073-20130315231954/@comment-5150073-20130321115939

But in that case, you reach not pentational arrays, but rather the structure Xvv^X, where v indicates the down-arrow, because your tetration is left-associative (called "weak tetration".) Just try to expand something like 3^^3 & 3. It would be expanded as (3^^2)^3 & 3 = (3^3)^3 & 3, right? If yes, then it is not 3^^3 & 3, but 3vv3 & 3.