On a transformation of Riordan moment sequences

2018/02/09 by Paul Barry, Barry, Paul · 1 citation
Mathematics · #05A15 #11B83 #11C20 #15B36 #44A10 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #Secondary 33C45

paper · pdf · doi:10.48550/arxiv.1802.03443

openalex publication_date 2018/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a transformation that associates certain exponential moment sequences with ordinary moment sequences in a natural way. The ingredients of this transformation are series reversion, the Sumudu transform (a variant of the Laplace transform), and the inverting of generating functions. This transformation also has a simple interpretation in terms of continued fractions. It associates lattice path objects with permutation objects, and in particular it associates the Narayana triangle with the Eulerian triangle.

Citations

• Production Matrices and Riordan Arrays
• The on-line encyclopedia of integer sequences

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• Three Études on a sequence transformation pipeline

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