User blog comment:Googleaarex/Extended Up Arrow Notation/@comment-5029411-20131130222905/@comment-25371339-20141014002749

If n!2[1] = (n![1])![1], then:

n!2[1] = aprox. (n^^n)^^n = aprox. n^^(n*2)

n![2] = aprox. n^^(n^2)

n![3] = aprox. n^^(n^2*2)

n![m] = aprox. n^^(n^2*m)