Geodesic
Exponential Riordan arrays and permutation enumeration
Journal of integer sequences, Tome 13 (2010) no. 9
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.
Classification : 05A15, 42C05, 11B83, 11C20, 15B05, 15B36, 20B30, 33C45
Keywords: permutation, integer sequence, orthogonal polynomials, moments, exponential riordan array, Hankel determinant, Hankel transform 
@article{JIS_2010__13_9_a1,
     author = {Barry,  Paul},
     title = {Exponential {Riordan} arrays and permutation enumeration},
     journal = {Journal of integer sequences},
     year = {2010},
     volume = {13},
     number = {9},
     zbl = {1201.05006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2010__13_9_a1/}
}
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Barry,  Paul. Exponential Riordan arrays and permutation enumeration. Journal of integer sequences, Tome 13 (2010) no. 9. http://geodesic.mathdoc.fr/item/JIS_2010__13_9_a1/