Journal of Integer Sequences, Vol. 13 (2010), Article 10.9.1

Exponential Riordan Arrays and Permutation Enumeration

Paul Barry
School of Science
Waterford Institute of Technology


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.

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(Concerned with sequences A000045 A000142 A000262 A000670 A007318 A021009 A094587 A094816 A111596 A111884.)

Received June 25 2010; revised version received September 13 2010. Published in Journal of Integer Sequences, December 5 2010.

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