The reciprocal super Catalan matrix studied by Prodinger is further generalized, introducing two additional parameters. Explicit formulae are derived for the $LU$-decomposition and their inverses, as well as the Cholesky decomposition. The approach is to use $q$-analysis and to leave the justification of the necessary identities to the $q$-version of Zeilberger's celebrated algorithm.
KILIÇ, EMRAH and ARIKAN, TALHA
"The generalized reciprocal super Catalan matrix,"
Turkish Journal of Mathematics: Vol. 40:
5, Article 3.
Available at: https://journals.tubitak.gov.tr/math/vol40/iss5/3