Bessel polynomials, double factorials and context-free grammars

TL;DR

This paper demonstrates how Bessel polynomials, double factorials, and Catalan triangle sequences can be generated using context-free grammars, linking combinatorial sequences with formal language theory.

Contribution

It introduces a novel method of generating classical combinatorial sequences through context-free grammars, bridging combinatorics and formal language theory.

Findings

Bessel polynomials can be generated by specific context-free grammars.

Double factorials are representable via context-free grammar rules.

Catalan triangle sequences can be derived using grammar-based methods.

Abstract

The purpose of this paper is to show that Bessel polynomials, double factorials and Catalan triangle can be generated by using context-free grammars.