User blog comment:DrCeasium/Extended Hyperfactorial Array Notation/@comment-5529393-20130329070454

As I mentioned in the comments of the other blog post, the strength of your previous notation is \(omega*2\) in the fast-growing hierarchy. More specifically, \( x_1 ! [x_2, ..., x_k]\) is at level \(omega + k - 2\). \(a!^n [x_1, x_2, ..., x_k]\) simply adds n-1 recursions to the previous notation, so it is at level \(omega + k + n - 2\), so your notation is still at level \(omega*2\) in the FGH.