Sums of Involving the Harmonic Numbers and the Binomial Coefficients

  Wuyungaowa, Sudan Wang

School of Mathematical Sciences, Inner Mongolia University, Hohhot, China.

DOI: 10.4236/ajcm.2015.52008                

Abstract

Let the numbers be defined by
, where
and are the exponential complete Bell polynomials. In this paper, by means of the methods of Riordan arrays, we establish general identities involving the numbers , binomial coefficients and inverse of binomial coefficients. From these identities, we deduce some identities involving binomial coefficients, Harmonic numbers and the Euler sum identities. Furthermore, we obtain the asymptotic values of some summations associated with the numbers by Darboux’s method.

Keywords

Harmonic Numbers, Euler Sum, Riordan Arrays, Asymptotic Values

Conflicts of Interest

The authors declare no conflicts of interest.

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