On members of Lucas sequences which are either products of factorials or product of middle binomial coefficients and Catalan numbers

Article Type

Research Article

Publication Title

Research in Number Theory

Abstract

Let {Un}n≥0 be a Lucas sequence. We show that if Un is a product of factorials, then n∈ { 1 , 2 , 3 , 4 , 6 , 8 , 12 }. Further we show that if Un is a product of Catalan numbers or the middle binomial coefficients, then n∈ { 1 , 2 , 3 , 4 , 6 , 8 , 12 , 16 }. Here the m- th middle binomial coefficient is Bm=(2mm) and the m- th Catalan number is Cm=1m+1(2mm).

DOI

10.1007/s40993-021-00257-x

Publication Date

6-1-2021

Comments

Open Access, Green

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