On Shapiro's Catalan convolution

George E. Andrews

doi:10.1016/j.aam.2010.07.003

On Shapiro's Catalan convolution

George E. Andrews

Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

L. Shapiro found an elegant formula for the self-convolution of the even subscripted terms in the Catalan sequence. This paper provides a natural q-analog of Shapiro's formula together with three proofs, one of which is purely combinatorial.

Original language	English (US)
Pages (from-to)	15-24
Number of pages	10
Journal	Advances in Applied Mathematics
Volume	46
Issue number	1-4
DOIs	https://doi.org/10.1016/j.aam.2010.07.003
State	Published - Jan 2011

All Science Journal Classification (ASJC) codes

Applied Mathematics

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10.1016/j.aam.2010.07.003

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title = "On Shapiro's Catalan convolution",

abstract = "L. Shapiro found an elegant formula for the self-convolution of the even subscripted terms in the Catalan sequence. This paper provides a natural q-analog of Shapiro's formula together with three proofs, one of which is purely combinatorial.",

author = "Andrews, \{George E.\}",

note = "Funding Information: E-mail address: [email protected]. 1 Partially supported by National Science Foundation Grant DMS-0801184.",

year = "2011",

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AB - L. Shapiro found an elegant formula for the self-convolution of the even subscripted terms in the Catalan sequence. This paper provides a natural q-analog of Shapiro's formula together with three proofs, one of which is purely combinatorial.

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UR - https://www.scopus.com/pages/publications/79953684548#tab=citedBy

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JF - Advances in Applied Mathematics

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ER -

On Shapiro's Catalan convolution

Abstract

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