Summary: We show that the generating function of the symmetric group with respect to five particular statistics gives rise to an exponential Riordan array, whose inverse is the coefficient array of the associated orthogonal polynomials. This also provides us with an LDU factorization of the Hankel matrix of the associated moments.

05A15, 42C05, 11B83, 11C20, 15B05, 15B36, 20B30, 33C45

permutation, integer sequence, orthogonal polynomials, moments, exponential riordan array, Hankel determinant, Hankel transform