[bbloomberg]

You can find the Catalan numbers buy computing 500,000,000,000 - Sqrt(500,000,000,000*500,000,000,000 - 1)....

http://people.csail.mit.edu/devadas/numerics_demo/chord.html

For an explanation better than I can provide of what they are and how it works, see 6.006 lecture 11 notes!

http://courses.csail.mit.edu/6.006/fall11/lectures/lecture11...