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.

References

On-Line Encyclopedia of Integer Sequences