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.
Modular periodicity of linear recurrenc e sequences
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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.