Journal of Integer Sequences, Vol. 10 (2007), Article 07.2.1

On Sums Involving Binomial Coefficients

S. Amghibech
Rue Wilfrid-Légaré
Québec, QC


We give closed forms for the series $\sum_{m=1}^{\infty}\frac{(2x)^{2m+2k}}{m^{2}(m+k) {2m \choose m}}$ and $\sum_{m=1}^{\infty}\frac{(2x)^{2m}(-1)^{m+k}}{m^{2}(m+k) {2m \choose
m}}$ for integers $k \geq 0$.

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Received December 26 2006; revised version received January 11 2007. Published in Journal of Integer Sequences January 15 2007.

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