No, the Ackermann numbers (from MathWorld) are defined as , because they are defined by arrow notation, and not box notation.
The numbers defined by have no name.
Andrew Robbins
The numbers defined by have no name.
Andrew Robbins
Name for sequence y=0[0]0. y=1[1]1, y=2[2]2, y= n[n]n, y=x[x]x, y=i[i]i, y=z[z]z etc?

No, the Ackermann numbers (from MathWorld) are defined as , because they are defined by arrow notation, and not box notation.
The numbers defined by have no name. Andrew Robbins 
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