The th Catalan number is given by:
where represents the binomial coefficient. The first several Catalan numbers are , , , , , , , , , ,…(see OEIS sequence http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=000108A000108 for more terms). The Catalan numbers are also generated by the recurrence relation
For example, , , etc.
The ordinary generating function for the Catalan numbers is
Interpretations of the th Catalan number include:
The Catalan sequence is named for Eugène Charles Catalan, but it was discovered in 1751 by Euler when he was trying to solve the problem of subdividing polygons into triangles.
- 1 Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. Concrete Mathematics. Addison-Wesley, 1998. http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0836.00001Zbl 0836.00001.
|Date of creation||2013-03-22 12:29:51|
|Last modified on||2013-03-22 12:29:51|
|Last modified by||bbukh (348)|