On the series $\pmb{\sum_{k = 1}^\infty \binom{3k}{k}^{-1}k^{-n} x^k}$

Abstract

In this paper we investigate the series $\sum_{k = 1}^\infty \binom{3k}{k}^{-1}k^{-n}x^k$. Obtaining some integral representations of them, we evaluated the sum of them explicitly for $n = 0, 1, 2$.