Journal of Integer Sequences, Vol. 21 (2018), Article 18.7.1

On a Transformation of Riordan Moment Sequences

Paul Barry
School of Science
Waterford Institute of Technology


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.

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(Concerned with sequences A000108 A000142 A000629 A000670 A001003 A001006 A001586 A005043 A006318 A008292 A021009 A049774 A052186 A052709 A060187 A064641 A090181 A097899 A111961 A123125 A129775 A131198 A173018.)

Received February 9 2018; revised versions received July 10 2018; July 16 2018. Published in Journal of Integer Sequences, August 23 2018.

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