A note on super Catalan numbers
Evangelos Georgiadis, Akihiro Munemasa, Hajime Tanaka
TL;DR
This paper reveals that super Catalan numbers can be expressed as specific values of Krawtchouk polynomials, providing a new perspective on their combinatorial significance.
Contribution
It establishes a novel connection between super Catalan numbers and Krawtchouk polynomials through an explicit expression involving a signed set.
Findings
Super Catalan numbers are special values of Krawtchouk polynomials
Derived an explicit expression for super Catalan numbers
Provides a new combinatorial interpretation
Abstract
We show that the super Catalan numbers are special values of the Krawtchouk polynomials by deriving an expression for the super Catalan numbers in terms of a signed set.
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