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%I #17 Aug 01 2019 00:20:33
%S 0,0,1,2,5,11,26,65,157,398,1017,2636,6891,18210,48459,129935
%N Number of power towers of x whose integrals over [0, 1] are above average.
%C Take n occurrences of x with exponentiation operators ^ between them and parenthesize them in all possible ways. Consider these expressions as functions on [0, 1], and remove duplicate functions. The number of remaining distinct functions are given by A000081. Now, integrate each function over [0, 1], find the average value of the results, and count the results that are above the average. This number gives a(n). Thus, a(n) < A000081(n).
%Y Cf. A000081.
%K nonn,more
%O 1,4
%A _Vladimir Reshetnikov_, Feb 26 2019
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