We consider sequences of images of Riordan arrays under some Riordan group automorphisms introduced by Bacher. We enclose their properties into several infinite square arrays which turn out to be of combinatorial interest. To illustrate our approach we consider Cameron and Nkwanta's sequence of generalized RNA arrays (whose first term is the well-known Nkwanta RNA array). Although this sequence of generalized RNA arrays was originally established as a sequence of pseudo-involutions, we show that it does not contain pseudo-involutions other than Nkwanta's array. We also show that these arrays are actually images of a new array under some of Bacher’s automorphisms. We study the combinatorics of some square matrices related to the generalized RNA arrays and to sequences of genuine pseudo-involutions generated by Nkwanta's array.