Journal of Integer Sequences, Vol. 15 (2012), Article 12.1.7

Series with Central Binomial Coefficients, Catalan Numbers, and Harmonic Numbers


Khristo N. Boyadzhiev
Department of Mathematics and Statistics
Ohio Northern University
Ada, Ohio 45810
USA

Abstract:

We present several generating functions for sequences involving the central binomial coefficients and the harmonic numbers. In particular, we obtain the generating functions for the sequences $\binom{2n}{n} H_{n} $, $\binom{2n}{n} \frac{1}{n} H_{n} $, $\binom{2n}{n} \frac{1}{n+1} H_{n} $ , and $\binom{2n}{n} n^{m} $. The technique is based on a special Euler-type series transformation formula.

Full version:  pdf,    dvi,    ps,    latex    

Received June 3 2011; revised version received December 16 2011. Published in Journal of Integer Sequences, December 27 2011.

Return to Journal of Integer Sequences home page