Fanation is the function a![b, 2], or a![b![b![b]]
Dufanation is the function a![b, 3], or a![b![b![b![b]]]]
Trefanation is the function a![b, 4], or a![b![b![b![b![b]]]]]
Bifanation is a![{b}], or a![b, b, b...b, b] with b b's.
Trikfanation is a![{{b}}], or a![{b}, {b}, {b}...{b}, {b}] with b {b}'s.
Tetfanation is a![{{{b}}}], or a![{{b}}, {{b}}, {{b}}...{{b}}, {{b}}] with b {{b}}'s.
Exfanation is a![bb], or a![{{{...{{{b}}}...}}}] with b sets of {}.
Cufanation is a![b2b], or a![{{{...{{{b}}}...}}}] with b+b sets of {}.
Tetrafanation is a![bb^2], or a![{{{...{{{b}}}...}}}] with b^2 sets of {}.
Exanexfanation is a![ba![b]], or a![{{{...{{{b}}}...}}}] with a![b] sets of {}.
Exabifanation is a![ba![{b}]], or a![{{{...{{{b}}}...}}}] with a![{b}] sets of {}.
Exacufanation is a![ba![{{b}}]], or a![{{{...{{{b}}}...}}}] with a![{{b}}] sets of {}.
Exatetfanation is a![ba![{{{b}}}]], or a![{{{...{{{b}}}...}}}] with a![{{{b}}}] sets of {}.
Cunexafanation is a![ba![bb]], or a![{{{...{{{b}}}...}}}] with a![{{{...{{{b}}}...}}}] with b sets of {}, sets of {}.