I create the fast-growing hierarchy-based notation that mimic the binary bisector notation, based on ordinals.
Definition:
B{0}(n) = 2^n
B{α+1}(n) = B{α}^n(n)
B{α}(n) = B{α[n]}(n), when α is a limit ordinal and α[n] is the nth term of fundamental sequence assigned to ordinal α.