The central binomial coefficients

Rule

Each term is: Take the number of combinations of 2n things taken n at a time

Known as: The central binomial coefficients

The central binomial coefficients

The central numbers on Pascal's triangle.

They occur as the solution to many problems, such as: The number of different minimal-length routes between opposite corners of a square grid of size n.

The first 16 terms (starting from n=0) are:

1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520

Example

To get the value for n=13:

  • Calculate the number of combinations of 2n things taken n at a time, giving 10400600.

So the result is 10400600.

References

On-Line Encyclopedia of Integer Sequences