
TL;DR
This paper introduces Fuss-Catalan triangles, a family of combinatorial arrays generalizing Catalan triangles, with explicit formulas and connections to lattice paths and known sequences for specific parameters.
Contribution
It defines a new class of triangles based on Fuss-Catalan numbers, providing explicit formulas and exploring their combinatorial properties and special cases.
Findings
Rows sum to Fuss-Catalan numbers
Explicit formulas for triangle entries
Connections to known sequences for small p
Abstract
For each we define by recurrence a triangle whose rows sum to the Fuss-Catalan numbers , generalizing the known Catalan triangle corresponding to the case . (In fact, has an explicit formula counting simple lattice paths). Moreover, for some small values of , the signed sums turn out to be known sequences. \end{abstract}
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Taxonomy
TopicsMathematics and Applications · Computational Geometry and Mesh Generation
