Summary: We analysed some series involving \[ {\binom {2k}k}^{-1}k^{-n} \text{ and } {\binom {2k}k}^{-2}k^{-n} \] and some other related series and derived the integral representations of those series considered by using some elementary properties of polylogarithms. The results we obtained show that all the integral representations involve so called log-sine terms. On using their representations we made some generalizations and closed form evaluations. We also obtained two new acceleration formulas for \({\zeta}\)(3) and Catalan’s constant \(G\).