Explicit Expressions for the First 20 Moments of the Area Under Dyck and Motzkin Paths
By AJ Bu, Shalosh B. Ekhad, and Doron Zeilberger
.pdf
.tex
Written: May 5, 2024
We show the utility of AJ Bu's recent
article for computing explicit expressions for the GENERATING functions of sums of powers of areas under Dyck
and Motzkin paths, by deducing from them explicit expressions for the actual sequences. This enables taking the
limits of the scaled moments and confirming, in an entirely elementary way, that they tend to those of the area under Brownian Excursion.
Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilerger, AJ Bu's website, and arxiv.org .
Maple package

qEWplus.txt,
for deriving (rigorously) explicit expressions for the moments of Dyck and Motzkin paths
Sample Input and Output for qEWplus.txt
If you want to see explicit expressions for the sum of the rth powers of areas under Dyck walks from 0 to 2n for r from 1 to 20
the input gives the
output
If you want to see explicit expressions for the sum of the rth powers of areas under Motzkin walks from 0 to n for r from 1 to 20
the input gives the
output
Doron Zeilberger's Home Page
AJ Bu's Home Page