User blog comment:King2218/BAL Notation Part 4/@comment-5029411-20140219134706

a{0[0,1]1}(0) = a{a[a]a}(0)

a{0[0,1]2}(0) = a{a[a]a[0,1]1}(0)

a{0[1,1]1}(0) = a{a[0,1]a...a[0,1]a}(0) (a a's)

a{0[0,2]1}(0) = a{a[a,1]a}(0)

a{0[0,0,1]1}(0) = a{a[a,a]a}(0)

Ultra n-bal = a{a[a[...a[a]a...]a]a}(0) (a nested)