One-$p$th Riordan Arrays in the Construction of Identities
Received:October 30, 2020  Revised:January 03, 2021
Key Word: Riordan array   one-$p$th Riordan arrays   $A$-sequence   generating function   identities  
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Author NameAffiliation
Tianxiao HE Department of Mathematics, Illinois Wesleyan University, Bloomington, Illinois 61702, USA 
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Abstract:
      For an integer $p\geq 2$ we construct vertical and horizontal one-$p$th Riordan arrays from a Riordan array. When $p=2$ one-$p$th Riordan arrays are reduced to well known half Riordan arrays. The generating functions of the $A$-sequences of vertical and horizontal one-$p$th Riordan arrays are found. The vertical and horizontal one-$p$th Riordan arrays provide an approach to construct many identities. They can also be used to verify some well known identities readily.
Citation:
DOI:10.3770/j.issn:2095-2651.2021.02.001
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