New Eulerian Numbers of Type $D$
Keywords: Eulerian numbers, Signed permutations, Moments of a probability measure
AbstractWe introduce a new array of type $D$ Eulerian numbers, different from that studied by Brenti, Chow and Hyatt. We find in particular the recurrence relation, Worpitzky formula and the generating function. We also find the probability distributions whose moments are Eulerian polynomials of type $A$, $B$ and $D$.