  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 $$ \frac{a_m(n)}{b_m(n)}x(n+m)+...+\frac{a_0(n)}{b_0(n)}x(n)= c(n),$$
where $a_i(n), b_i(n), c(n)$ are polynomials. Our algorithm improves Abramov's
universal denominator.
