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?

[GFR]

Dear Ivars:

0[0]0 = ??? (I try to avoid troubles ... )
1[1]1 = 1+1 = 2
2[2]2 = 2*2 = 4
3[3]3 = 3^3 = 27
4[4]4 = 4#4 = 4^[4^[4^4]]] .... uuuuuhhhhh !!!
......
oo[w]oo = ...... infinite-omega-infinite (Qickfur said that it is still enumerable! I think he is right!). Actually, we could write it as oo[oo]oo, but I think that the entity between the brackets is an ordinal. Am I wrong? Maybe yes ! Ops, suicide comment: how about s=0, the 0-th hyperop?

GFR