A generalization of the Kreweras triangle through the universal ${\text{sl}}_2$ weight system

In the theory of finite order knot invariants, the universal ${\text{sl}}_2$ weight system maps the chord diagrams to polynomials in a single variable with integer coefficients. In this paper, we define a family of polynomials that generalize the Kreweras triangle (known to refine the normalized median Genocchi numbers), and we show how it appears in this weight system.