Dumont and Foata introduced in 1976 a three-variable symmetric refinement of
Genocchi numbers, which satisfies a simple recurrence relation. A six-variable
generalization with many similar properties was later considered by Dumont.
They generalize a lot of known integer sequences, and their ordinary generating
function can be expanded as a Jacobi continued fraction.
We give here a new combinatorial interpretation of the six-variable
polynomials in terms of the alternative tableaux introduced by Viennot. A
powerful tool to enumerate alternative tableaux is the so-called "matrix
Ansatz", and using this we show that our combinatorial interpretation naturally
leads to a new proof of the continued fraction expansion.Comment: 17 page
