On the -shifted central triangles of a Riordan array

P Barry - arXiv preprint arXiv:1906.01328, 2019 - arxiv.org
arXiv preprint arXiv:1906.01328, 2019arxiv.org
Let $ A $ be a proper Riordan array with general element $ a_ {n, k} $. We study the one
parameter family of matrices whose general elements are given by $ a_ {2n+ r, n+ k+ r} $.
We show that each such matrix can be factored into a product of a Riordan array and the
original Riordan array $ A $, thus exhibiting each element of the family as a Riordan array.
We find transition relations between the elements of the family, and examples are given.
Lagrange inversion is used as a main tool in the proof of these results.
Let be a proper Riordan array with general element . We study the one parameter family of matrices whose general elements are given by . We show that each such matrix can be factored into a product of a Riordan array and the original Riordan array , thus exhibiting each element of the family as a Riordan array. We find transition relations between the elements of the family, and examples are given. Lagrange inversion is used as a main tool in the proof of these results.
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