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Closed forms for convolutions of Catalan numbers

  • N. Gauthier (a1)

Extract

In Catalan numbers with applications [1], Thomas Koshy gives a clear and accessible account of some of the important characteristics of Catalan numbers. The author also discusses the significance of these numbers for mathematicians, scientists, engineers and amateur enthusiasts alike. The general contents of his book are reviewed in [2]. Catalan numbers, which are named after the mathematician Eugene Catalan (1814-1894), have very interesting and sometimes surprising properties.

Catalan numbers occur in combinatorial mathematics, in particular, where they show up as a natural number sequence that arises in counting problems that usually involve recursively-defined objects.

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References

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1. Koshy, T., Catalan numbers with applications, Oxford University Press (2009).
2. Gauthier, N., Thomas Koshy's Catalan numbers with applications, The Fibonacci Quarterly 48 (February 2010) pp. 8586.
3. Stanley, Richard and Weisstein, Eric W., Catalan Number, from MathWorld-A Wolfram Web Resource. http://mathworld.wolfram.com/CatalanNumber.html
5. Abramowitz, M. and Stegun, I. A., Handbook of mathematical functions, New York: Dover Publications (1965).
6. Mangulis, V., Handbook of series for scientists and engineers, New York: Academic Press (1965).

Closed forms for convolutions of Catalan numbers

  • N. Gauthier (a1)

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