Fuss-Catalan matrices, their weighted sums, and stabilizer subgroups of the Riordan group

In this paper, we present the Riordan arrays called Fuss-Catalan matrices which are constructed by the convolutions of the generating functions of the Fuss-Catalan numbers. We also discuss weighted sums of the Fuss-Catalan matrices, using such matrices as transformations of recursive sequences, and their connection with stabilizer subgroups of the Riordan group.