A matrix with sums of Catalan numbers -- LU-decomposition and determinant
Combinatorics
2021-06-15 v2
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.
Cite
@article{arxiv.2104.03921,
title = {A matrix with sums of Catalan numbers -- LU-decomposition and determinant},
author = {Helmut Prodinger},
journal= {arXiv preprint arXiv:2104.03921},
year = {2021}
}