Weighted Catalan numbers satisfy the same 2-adic valuations as Catalan numbers under weaker conditions than previously known, and their periodicity modulo integers is fully characterized and applied to Morse link numbers.
Divisibility of generalized Catal an numbers
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Arithmetic of weighted Catalan numbers
Weighted Catalan numbers satisfy the same 2-adic valuations as Catalan numbers under weaker conditions than previously known, and their periodicity modulo integers is fully characterized and applied to Morse link numbers.