By combining inverse series relations with binomial convolutions and telescoping method, moments of Catalan numbers are evaluated, which resolves a problem recently proposed by Gutiérrez et al. [J.M. Gutiérrez, M.A. Hernández, P.J. Miana, N. Romero, New identities in the Catalan triangle, J. Math. Anal. Appl. 341 (1) (2008) 52-61]. © 2008 Elsevier Inc. All rights reserved.
Chen, X., & Chu, W. (2009). Moments on Catalan numbers. Journal of Mathematical Analysis and Applications, 349(2), 311–316. https://doi.org/10.1016/j.jmaa.2008.08.042