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%I #22 Feb 20 2013 16:42:36
%S 1,1,2,4,9,20,47,111,271,670,1685,4295,11074,28824
%N Number of distinct values taken by r^r^...^r where r=1/2 (with n r's and parentheses inserted in all possible ways).
%t f[1] = {1/2}; f[n_] := f[n] = Union[Flatten[Table[Outer[Power, f[k], f[n - k]], {k, n - 1}]], SameTest -> Equal]; Table[Length[f[n]], {n, 1, 10}] (* Vladimir Reshetnikov, Nov 01 2011 *)
%Y Cf. A002845, A082499.
%K nonn,more
%O 1,3
%A _Vladimir Reshetnikov_, Oct 27 2011
%E a(13)-a(14) from _Alois P. Heinz_, Feb 20 2013
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