English

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.

Keywords

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}
}