an:00790762
Zbl 0832.05007
Sprugnoli, Renzo
Riordan arrays and the Abel-Gould identity
EN
Discrete Math. 142, No. 1-3, 213-233 (1995).
00027770
1995
j
05A19 05A15
generating functions; Riordan arrays; Lagrange inversion formula; Abel- Gould identity; Stirling numbers
Riordan arrays were introduced in [\textit{L. V. Shapiro}, \textit{S. Getu}, \textit{W.-J. Woan} and \textit{L. C. Woodson}, The Riordan group, Discrete Appl. Math. 34, No. 1-3, 229-239 (1991; Zbl 0754.05010)] and further developed by the author of the present paper in a previous work [the author, Riordan arrays and combinatorial sums, Discrete Math. 132, No. 1- 3, 267-290 (1994; Zbl 0814.05003)]. Here the author uses the Lagrange inversion formula and his previous results to obtain a general formula from which the so-called Abel-Gould identity and many other identities, including some involving Stirling numbers of both kinds, fall out as special cases.
T.R.Walsh (Montreal)
Zbl 0754.05010; Zbl 0814.05003