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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.

05A19 Combinatorial identities, bijective combinatorics
05A15 Exact enumeration problems, generating functions
Full Text: DOI
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[9] Sprugnoli, R., Riordan arrays and combinatorial sums, Discrete math., 132, 267-290, (1994) · Zbl 0814.05003
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