Shapiro, Louis W. A short proof of an identity of Touchard’s concerning Catalan numbers. (English) Zbl 0337.05012 J. Comb. Theory, Ser. A 20, 375-376 (1976). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 17 Documents MSC: 05A19 Combinatorial identities, bijective combinatorics 05A10 Factorials, binomial coefficients, combinatorial functions 11B39 Fibonacci and Lucas numbers and polynomials and generalizations PDF BibTeX XML Cite \textit{L. W. Shapiro}, J. Comb. Theory, Ser. A 20, 375--376 (1976; Zbl 0337.05012) Full Text: DOI References: [1] Izbicki, H, Über unterbaumes eines baumes, Monatshefte F. math., 74, 56-62, (1970) · Zbl 0209.28102 [2] Motzkin, T, Relations between hypersurface cross ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for non-associative products, Bull. amer. math. soc., 54, 352-360, (1948) · Zbl 0032.24607 [3] Riordan, J, A note on Catalan parentheses, Amer. math. monthly, 80, 904-906, (1973) · Zbl 0301.05003 [4] \scL. Shapiro, Catalan numbers and total information numbers, in “Proceedings of the Sixth Southeastern Conference on Combinatorics, Graph Theory, and Computing,” to appear. · Zbl 0327.05013 [5] Touchard, J, Sur certaines équations fontionnelles, (), 465 [6] Yaglom, A; Yaglom, I, () This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.