A new algorithm for the recursion of multisums with improved universal denominator

The purpose of the paper is to introduce two new algorithms. The first one computes a linear recursion for proper hypergeometric multisums, by treating one summation variable at a time, and provides rational certificates along the way. A key part in the search of a linear recursion is an improved universal denominator algorithm that constructs all rational solutions $x(n)$ of the equation $$\frac{a_m(n)}{b_m(n)}x(n+m)+\mathrm{.}\mathrm{.}\mathrm{.}+\frac{a_0(n)}{b_0(n)}x(n)=c(n),$$ where $a_i(n),b_i(n),c(n)$ are polynomials. Our algorithm improves Abramov’s universal denominator.