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A matrix with sums of Catalan numbers -- LU-decomposition and determinant (2104.03921v2)
Published 6 Apr 2021 in math.CO
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.