Summary: Entringer numbers occur in the André permutation combinatorial set-up under several forms. This leads to the construction of a matrix refinement of the tangent (respectively secant) numbers. Furthermore, closed expressions for the three-variate exponential generating functions for pairs of so-called Entringerian statistics are derived.
Mathematics Subject Classification
05A15, 05A30, 11B68, 33B10
entringer numbers, tangent and secant numbers, alternating permutations, andré permutations, seidel matrix sequence, increasing binary trees, greater neighbor of maximum, spike, pit, tight permutations, hooked permutations, seidel triangle sequence, formal Laplace transform