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A short proof of an identity of Touchard’s concerning Catalan numbers. (English) Zbl 0337.05012

MSC:
05A19 Combinatorial identities, bijective combinatorics
05A10 Factorials, binomial coefficients, combinatorial functions
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
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[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, ()
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