Abstract
Historically, there exist two versions of the Riordan array concept. The older one (better known as recursive matrix) consists of bi-infinite matrices ( d n , k ) n , k ∈ Z ( k > n implies d n , k = 0 ), deals with formal Laurent series and has been mainly used to study algebraic properties of such matrices. The more recent version consists of infinite, lower triangular arrays ( d n , k ) n , k ∈ N ( k > n implies d n , k = 0 ), deals with formal power series and has been used to study combinatorial problems. Here we show that every Riordan array induces two characteristic combinatorial sums in three parameters n , k , m ∈ Z . These parameters can be specialized and generate an indefinite number of other combinatorial identities which are valid in the bi-infinite realm of recursive matrices.
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