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Riordan arrays and the Abel-Gould identity. (English) Zbl 0832.05007
Riordan arrays were introduced in [L. V. Shapiro, S. Getu, W.-J. Woan and 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.

MSC:
05A19 Combinatorial identities, bijective combinatorics
05A15 Exact enumeration problems, generating functions
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References:
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