Maximal number of regions obtained by joining n points around a circle by straight lines Let's define f(n) as the aximal number of regions obtained by joining n points around a circle by straight lines. For example, two points would split the circle into two pieces, three into four, like this:


Make sure when you are drawing the lines, you don't have an intersection of more than two lines.

Your task

Given a number n, print f(n).

Test cases:

 n | f(n)   
---+-----
 1 |   1
 2 |   2
 3 |   4
 4 |   8
 5 |  16
 6 |  31
 7 |  57
 8 |  99
 9 | 163


You can see more here.

Using built-in sequence generators is not allowed.

Remember, this is code-golf, so the code with the smallest number of bytes wins.

If you guys want the formula, here it is:
Mathematica, 23 bytes
Tr@Binomial[#,{0,2,4}]&amp;

Uses the formula in the question.