Sums of powers of Catalan triangle numbers

We present identities for sums (and alternating sums) of Cm,k, squares and cubes of Cm,k and, consequently, for Bn,k and An,k. In particular, one of these identities solves an open problem posed in Gutiérrez et al. (2008). We also give some identities between (Cm,k)m≥1,k≥0 and harmonic numbers (Hn)n≥1. Finally, in the last section, new open problems and identities involving (Cn)n≥0 are conjectured.