A CASE STUDY IN DETERMINANT EVALUATIONS

In this case study, we hope to elucidate three versatile and powerful tools (Dodgson's condensation, the holonomic ansatz and constant term evaluations) to operate in tandem in proving a certain determinantal formula conjectured by the first author. We also include a postscript describing yet another, more methodological, toolbox for evaluating determinants: 'ask determinant-guru, Christian Krattenthaler', but advise people only to use it as a last resort, since if we would have used this last method right away, we would not have had the fun of doing it all by ourselves. Throughout this paper, the reader finds new proofs of interest while marching along the untrodden ways of our journey.