Journal of Integer Sequences, Vol. 16 (2013), Article 13.5.1 |

School of Science

Waterford Institute of Technology

Ireland

**Abstract:**

We use the Lagrange-Bürmann inversion theorem to characterize the
generating function of the central coefficients of the elements of the
Riordan group of matrices. We apply this result to calculate the
generating function of the central elements of a number of explicit
Riordan arrays, defined by rational expressions, and in two cases we
use the generating functions thus found to calculate the Hankel
transforms of the central elements, which are themselves expressible as
combinatorial polynomials. We finally look at two cases of Riordan
arrays defined by non-rational expressions. The last example uses our
methods to calculate the generating function of
.

(Concerned with sequences A000045 A000108 A000984 A001850 A005809 A007318 A084774 A092392 A174687.)

Received January 2 2013;
revised version received May 2 2013.
Published in *Journal of Integer Sequences*, May 8 2013.

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