The ψ-Notation

Another notation I made.

Level 1

• ψ_a = a↑^aa
• ψ_a,b = ψ_{ψ...(b levels)a}
• ψ_a,b,c = ψ_{a,ψa,ψ ... (c levels)b}

All further ones work the same, but the last entry gets recursively repalced "lastentry" times.

Level 2

• ψ[n] = ψ_n
• ψ[n,m] = ψ_{n,n,n,n,n,n...} (m n's in array)
• ψ[ [n] ] = ψ[ψ[n]] (works the same way for larger ammount of brackets)
• ψ[n]#x = ψ[ [ [ [ .... (x brackets ....[n]]
• ψ[ [n,m] ] = ψ[n,ψ[n,ψ[ ... (m ψ's) ...[n]]
• ψ[n,m]#x = ψ[ [ [ [ [ ... (x brackets) ... [n,m]]

• ψ[]#{z}z = ψ[]###... (z #'s) ...###z
• ψ[n,m,p] = ψ[n,m]#{p}p
• ψ[n,m,p,j] = ψ[n,m,p]#{ψ[n,m]}j
• ψ[n,m,p,j,j2] = ψ[n,m,p,j]#{ψ[n,m,p]}j2
• Etc for more entries.