  The ECO method and the theory of Catalan-like numbers introduced by Aigner
seems two completely unrelated combinatorial settings. In this work we try to
establish a bridge between them, aiming at starting a (hopefully) fruitful
study on their interactions. We show that, in a linear algebra context (more
precisely, using infinite matrices), a succession rule can be translated into a
(generalized) Aigner matrix by means of a suitable change of basis in the
vector space of one-variable polynomials. We provide some examples to
illustrate this fact and apply it to the study of two particular classes of
succession rules.
