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Tribinomial coefficients and Catalan numbers

Published online by Cambridge University Press:  01 August 2016

Thomas Koshy  and
Mohammad Salmassi
Thomas Koshy
Affiliation:
Framingham State College, 100 State St, Framingham MA10701-9101 USA
Mohammad Salmassi
Affiliation:
Framingham State College, 100 State St, Framingham MA10701-9101 USA
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Extract

The concept of the ordinary binomial coefficient

can be employed to construct an interesting family of positive integers. Such a family was introduced around 1974 by W. Hansell using the triangular numbers , where we call them tribinomial coefficients since they are binomial coefficients for triangular numbers. To this end, first we define corresponding to and For example,

Type
Articles
Information
The Mathematical Gazette , Volume 93 , Issue 528 , November 2009 , pp. 449 - 455
Copyright
Copyright © The Mathematical Association 2009

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References

1. Graham, R. L. et al, Concrete mathematics, Addison-Wesley, Reading, MA (1990).Google Scholar
2. Hoggatt, H. E. Jr., Triangular numbers, Fibonacci Quarterly 12 (October 1974) pp. 221–230.Google Scholar
3. Koshy, T., Catalan numbers with applications, Oxford University Press, New York (2009).Google Scholar
4. Koshy, T. and Salmassi, M., Parity and primality of Catalan numbers, College Mathematics Journal 36 (November 2005) pp. 52–53.Google Scholar
5. Koshy, T., Elementary number theory with applications (2nd edn.), Academic Press, Burlington (2007).Google Scholar