Cigler, J.; Krattenthaler, C. Some determinants of path generating functions. (English) Zbl 1227.05067 Adv. Appl. Math. 46, No. 1-4, 144-174 (2011). Summary: We evaluate four families of determinants of matrices, where the entries are sums or differences of generating functions for paths consisting of up-steps, down-steps and level steps. By specialisation, these determinant evaluations have numerous corollaries. In particular, they cover numerous determinant evaluations of combinatorial numbers-most notably of Catalan, ballot, and of Motzkin numbers-that appeared previously in the literature. Cited in 2 ReviewsCited in 16 Documents MSC: 05A19 Combinatorial identities, bijective combinatorics 05A10 Factorials, binomial coefficients, combinatorial functions 05A15 Exact enumeration problems, generating functions 11C20 Matrices, determinants in number theory 15A15 Determinants, permanents, traces, other special matrix functions Keywords:Hankel determinants; Catalan numbers; ballot numbers; Motzkin numbers; Motzkin paths; non-intersecting lattice paths Software:DODGSON; DET PDFBibTeX XMLCite \textit{J. Cigler} and \textit{C. Krattenthaler}, Adv. Appl. Math. 46, No. 1--4, 144--174 (2011; Zbl 1227.05067) Full Text: DOI arXiv References: [1] Aigner, M., Catalan and other numbers: a recurrent theme, (Crapo, H.; Senato, D., Algebraic Combinatorics and Computer Science (2001), Springer-Verlag: Springer-Verlag Berlin), 347-390 · Zbl 0971.05002 [2] Amdeberhan, T.; Zeilberger, D., Determinants through the looking glass, Adv. in Appl. 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