The Catalan numbers
Rule
Each term is: Take the number of combinations of 2n things taken n at a time, then divided by n+1
Known as: The Catalan numbers
The first 16 terms (starting from n=0) are:
1 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845
Example
To get the value for n=12:
- Calculate the number of combinations of 2n things taken n at a time, giving 2704156.
- Divide by n+1, or 13, giving 208012.
So the result is 208012.