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We define \(f_5(n)\), \(f_6(n)\), \(f_7(n)\),... factorial.

We continue factorial:

n!Lm = n!n,n...n,n (m n's)

n!Lx,y = n!Lx!Ly

n!Lx,y,z = n!Lx!Ly!Lz

n!LLm = n!Ln,n...n,n (m n's)

The growth rate is \(f_\omega(n)\) > n!LL...LLn (n-2 n's)

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