In this paper, we present an involution on some kind of colored $k$-ary trees which provides a combinatorial proof of a combinatorial sum involving the generalized Catalan numbers $C_{k,γ}(n)=\fracγ{k n+γ}{k n+γ\choose n}$. From the combinatorial sum, we refine the formula for $k$-ary trees and obtain an implicit formula for the generating function of the generalized Catalan numbers which obviously implies a Vandermonde type convolution generalized by Gould. Furthermore, we also obtain a combinatorial sum involving a vector generalization of the Catalan numbers by an extension of our involution.