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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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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] L. Shapiroin; L. Shapiroin · Zbl 0327.05013
[5] Touchard, J., Sur Certaines Équations Fontionnelles, (Proc. Int. Math. Congress, Toronto (1924), Vol. 1 (1928)), 465
[6] Yaglom, A.; Yaglom, I., (Challenging Mathematical Problems with Elementary Solutions, Vol. I (1964), Holden-Day: Holden-Day San Francisco) · Zbl 0123.24201
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