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A306563
Number of power towers of x whose integrals over [0, 1] are above average.
0
0, 0, 1, 2, 5, 11, 26, 65, 157, 398, 1017, 2636, 6891, 18210, 48459, 129935
OFFSET
1,4
COMMENTS
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).
CROSSREFS
Cf. A000081.
Sequence in context: A192400 A308154 A182053 * A308060 A235496 A025245
KEYWORD
nonn,more
AUTHOR
STATUS
approved