We characterize certain Riordan arrays by their $A$-matrices and $\rho$ sequences. We conjecture the form of a generic $A$-matrix which leads to Somos $4$ sequences. We find an $A$-matrix that produces a Riordan quasi-involution, and we study the $A$-matrices and $\rho$ sequences of the moment matrices of certain perturbed orthogonal polynomials.
Generalized Catalan recurrences, Riordan arrays, elliptic curves, and orthogonal polynomials
A Note on Riordan Arrays with Catalan Halves
Embedding structures associated with Riordan arrays and moment matrices
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