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 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.