Journal of Integer Sequences, Vol. 16 (2013), Article 13.5.6

On the Inverses of a Family of Pascal-Like Matrices Defined by Riordan Arrays

Paul Barry
School of Science
Waterford Institute of Technology


We study a number of characteristics of the inverses of the elements of a family of Pascal-like matrices that are defined by Riordan arrays. We give several forms of the bivariate generating function of these inverses, along with four different closed-form expressions for the general element of the inverse. We study the row sums and the diagonal sums of the inverses, and the first column sequence. We exhibit the elements of the first column sequence of the inverse matrix as the moments of a family of orthogonal polynomials, whose coefficient array is again a Riordan array. We also give the Hankel transform of these latter sequences. Other related sequences are also studied.

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(Concerned with sequences A000045 A000108 A001850 A007318 A008288 A009766 A033282 A086810 A103209 A114710.)

Received January 15 2013; revised versions received April 15 2013; May 6 2013. Published in Journal of Integer Sequences, May 25 2013.

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