Geodesic
On sums involving binomial coefficients
Journal of integer sequences, Tome 10 (2007) no. 2
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 $k \geq 0$.
Classification : 11B65
Keywords: binomial coefficients, integral 
@article{JIS_2007__10_2_a7,
     author = {Amghibech,  S.},
     title = {On sums involving binomial coefficients},
     journal = {Journal of integer sequences},
     year = {2007},
     volume = {10},
     number = {2},
     zbl = {1127.11015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_2_a7/}
}
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Amghibech,  S. On sums involving binomial coefficients. Journal of integer sequences, Tome 10 (2007) no. 2. http://geodesic.mathdoc.fr/item/JIS_2007__10_2_a7/