English

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