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Journal of Discrete Mathematics
Volume 2013 (2013), Article ID 373927, 10 pages
http://dx.doi.org/10.1155/2013/373927
Research Article

Sums of Products of Cauchy Numbers, Including Poly-Cauchy Numbers

Graduate School of Science and Technology, Hirosaki University, Hirosaki 036-8561, Japan

Received 24 July 2012; Accepted 24 October 2012

Academic Editor: Gi Sang Cheon

Copyright © 2013 Takao Komatsu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate sums of products of Cauchy numbers including poly-Cauchy numbers: . A relation among these sums shown in the paper and explicit expressions of sums of two and three products (the case of and that of described in the paper) are given. We also study the other three types of sums of products related to the Cauchy numbers of both kinds and the poly-Cauchy numbers of both kinds.