Bijective Proofs of Identities from Colored Binary Trees

In this note, we give a parity reversing involution on colored binary trees which leads to a combinatorial interpretation of Formula (1.2). We make a simple variation of the bijection between colored ternary trees and binary trees proposed by Sun [2] and find a correspondence between certain class of binary trees and the set of colored 5-ary trees. The generalization of the parity reversing involution and the bijection to forests of colored binary trees and forests of colored 5-ary trees leads to a bijective proof of Formula (1.1).