Walking into an absolute sum
Number Theory
2007-06-13 v1 Statistics Theory
Statistics Theory
Abstract
We investigate a combinatorial sum that can be interpreted as the moments of a random variate, measuring the absolute distance to the origin in a symmetric Bernoulli random walk. These sums can be characterized by polynomials related to the Dumont-Foata polynomials. The sums corresponding to the odd moments have a connection to the Gandhi polynomials and Genocchi numbers.
Keywords
Cite
@article{arxiv.math/0606080,
title = {Walking into an absolute sum},
author = {Hans J. H. Tuenter},
journal= {arXiv preprint arXiv:math/0606080},
year = {2007}
}
Comments
Related sequence in "The On-Line Encyclopedia of Integer Sequences" is A083061. See http://www.research.att.com/~njas/sequences/A083061