On one property of Catalan numbers

2025/07/28 by Kochetkov, Yury
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.20584

Abstract

We give a new proof of the following statement: the Catalan number C_n is divisible by n+2, if n is odd and n\not≡ 1 mod 3.

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• The valuation of Catalan numbers
• Notes on Divisibility of Catalan Numbers
• Are the Catalan Numbers a Linear Recurrence Sequence?
• The Catalan numbers have no forbidden residue modulo primes