User blog comment:Googleaarex/Stronger Hyperfactorial Array Notation/@comment-25418284-20131213221550/@comment-25418284-20131215023743

@aarex Sorry, but that's not what I was asking for. I'd like to see a formal, inductive definition that does NOT use "..." or "n times" or "n nested". Do you know how to do that?

Ellipses are at worst ambiguous, awkward, or notationally confusing, and in general just plain informal. They certainly have their place, such as when trying to explain something to laymen, but you should really use a formal definition when presenting your own notation.