A306563 - OEIS

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A306563

Number of power towers of x whose integrals over [0, 1] are above average.

0, 0, 1, 2, 5, 11, 26, 65, 157, 398, 1017, 2636, 6891, 18210, 48459, 129935

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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).

LINKS

Table of n, a(n) for n=1..16.

CROSSREFS

Cf. A000081.

Sequence in context: A192400 A308154 A182053 * A308060 A235496 A025245

Adjacent sequences: A306560 A306561 A306562 * A306564 A306565 A306566

KEYWORD

nonn,more

AUTHOR

Vladimir Reshetnikov, Feb 26 2019

STATUS

approved