On Shapiro's Catalan convolution

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11 Scopus citations


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 languageEnglish (US)
Pages (from-to)15-24
Number of pages10
JournalAdvances in Applied Mathematics
Issue number1-4
StatePublished - Jan 2011

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


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