A matrix with sums of Catalan numbers -- LU-decomposition and determinant

Helmut Prodinger

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arXiv · 2104.03921

A matrix with sums of Catalan numbers -- LU-decomposition and determinant

Helmut Prodinger

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Abstract

Following Benjamin et al., a matrix with entries being sums of two neighbouring Catalan numbers is considered. Its LU-decomposition is given, by guessing the results and later prove it by computer algebra, with lots of human help. Specializing a parameter, the determinant turns out to be a Fibonacci number with odd index, confirming earlier results, obtained back then by combinatorial methods.

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Helmut Prodinger. 2021-06-13. A matrix with sums of Catalan numbers -- LU-decomposition and determinant. https://arxiv.org/abs/2104.03921

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