Determinants through the looking glass

Using a recurrence derived from Dodgson's Condensation Method, we provide n umerous explicit evaluations of determinants. They were all conjectured, an d then rigorously proved, by computer-assisted methods, that should be amen able to full automation. We also mention a first step towards that goal, ou r Maple package, DODGSON, that automates the special case of Hankel and Toe plitz hypergeometric determinants. (C) 2001 Academic Press.