Prof. Guoce Xin，Department of Mathematics, Capital Normal University Beijing, China

Hankel determinants by a new type of continued fractions

Many methods have been develped to evaluate the Hankel determinants associated to an ordinary generating function. The method of S type and J type continued fractions is very useful, elegant and has combinatorial interpretations. However, such continued fractions only exist if all of the Hankel determinants do not vanish. By using simple transformation rules, we develop new type of continued fractions. As applications, we evaluate some hard Hankel determinants, in particular, we prove a Somos' conjectured Hankel determinants representation of the Somos-4 sequences.