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

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