User blog comment:DrCeasium/new hyperfactorial array notation/@comment-5529393-20130416153852/@comment-5529393-20130416180720

Hmm, I don't think the nesting hierarchy actually helps, because f_n is just n-1 levels in the FGH beyond f_1. So, if we are at the ath row of the array, then we are dealing with functions like f_{w^w^(a-1)} (or higher, if your claims are correct), and using the (a-1) stage of the nesting hierarchy will just take that to f_{w^w^(a-1) + a-2}, which is a trivial difference.

I'm analyzing your arrays again, but I have a question:  what do you do when the the first entry is an array, e.g. 3![[3], 1, 2].