User blog comment:Nayuta Ito/Intuitive Arrow Notation/@comment-11227630-20171017075941

This notation doesn't go through "linear omega level". But "linear omega level" goes up to (but not including) $$\omega^2$$.
 * n[n]n has growth rate $$\omega$$
 * n[n,n]n has growth rate $$\omega+1$$
 * n[n,n,n]n has growth rate $$\omega+2$$
 * n[n,n,n,n]n has growth rate $$\omega+3$$
 * n[n,n,...n,n]n with n n's has growth rate $$\omega2$$