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At Extended Factorial

1 --> n!

2 --> (n!)!

3 --> ((n!)!)!

m -- > n!m

n -- > n!n

At Pentation-Extended Factorial

n,1 -- > n!n!

n,2 -- > n!n!2

n,m -- > n!n!m

n,n -- > n!n!n

a,b,c -- > n!a!b!c

n,n,m -- > n!n!n!m

a,b,...,y,z -- > n!a!b!...y!z

The growth rate is \(f_4(n) > n!_{n,n,...,n,n}\) (n n's)

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