Some Pascal’s like triangles
In this article, we delve into the fascinating world of numerical triangles similar to Khayyam-Pascal triangle. Our focus is on triangles that are comprised of natural numbers. Along with a combi-natorial interpretation, we also propose an algebraic interpretation for the elements in most cases. We explore in details the triangle of coefficients of Chebyshev polynomials (Chebyshev triangle). Through our analysis, we derive a recursive relation for its elements. This finding sheds new light on the properties of this intriguing numerical construction. To further enhance our understanding of these triangles, we also present new images related to the Catalan, Bell, and Chebyshev triangles. These images provide a clearer visualization of the numerical triangle construction. Overall, this article offers a comprehensive exploration of numerical triangles similar to Khayyam-Pascal triangle and examine some of their properties and relationships for better understanding of these constructions.
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