Alonso Del Arte notes on SeqFan that this "nice" count (authored recently by Vladimir Reshetnikov) of the "number of distinct values taken by i^i^...^i (with n i's and parentheses inserted in all possible ways*) where i = sqrt(-1) and ^ denotes the principal value of the power function" [A198683: 1, 1, 2, 3, 7, 15, 34, 77, 187, 462, 1152, 2926, ...] breaks down calculating the next (thirteenth) term, using the Mathematica formulation f[1] = {I}; f[n_] := f[n] = Union[Flatten[Table[Outer[Power, f[k], f[n-k]], {k, n-1}]], SameTest -
Equal]; Table[Length[f[n]], {n, 13}], with overflow errors. I'm wondering if anyone here is able to determine subsequent terms.
*Example: a(4) = 3: there are 5 possible parenthesizations but they give only 3 distinct values: i^(i^(i^i)), i^((i^i)^i) = ((i^i)^i)^i, (i^i)^(i^i) = (i^(i^i))^i.