User blog comment:Googleaarex/Extended Up Arrow Notation/@comment-5029411-20131130222905/@comment-25371339-20141019213550

Wait. My comparisons are wrong.

n! --> n^n --> f_2(n)

n!2 --> (n^n)^(n^n) --> f_2(f_2(n))

n![1] --> n^^n --> f_3(n)

n!2[1] --> (n^^n)^^(n^^n) --> f_3(f_3(n))

n![2] --> n^^^n --> f_4(n)

n![3] --> n^^^^n --> f_5(n)

Let ^(#)^ = ^_#

n![m] --> n^(1)^(m-1) --> f_m-2(n)

n![n] --> n^(1)^n --> f_n(n) = f_w(n)