2016/07/19 by Shalosh B. Ekhad, Doron Zeilberger, Ekhad, Shalosh B. +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1607.05776
9 pages. Accompanied by a Maple package available from http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/a435.html . Exclusively published in the Personal journal of Shalosh B. Ekhad and Doron Zeilberger and this arxiv. This version corrects a slip-of-the-tongue error in the abstract ("probability density function" was erroneously written "probability generating function")
arxiv created 2016/07/24 · arxiv updated 2016/07/26
In this tribute to Neil Sloane, we revisit the first sequence in the On-Line Encyclopedia of Integer Sequences, sequence A435 (1, 8, 78, 944, 13800, 237432, 4708144, 105822432, ...), that he encountered when he was a graduate student, and when normalized gives the average total height of rooted labeled trees. We state rigorously-computed explicit expressions for the first twelve moments of the random variable `total height' on rooted labeled trees, and pledge to donate to the OEIS 100 dollars in honor of the first to find an explicit expression for the probability density function of the limiting scaled probability distribution, as n goes to infinity.