How many signs?

How many different signs are there? Or, to make the question slightly more definite, how many signs can you make with 1 circle, 2 circles, 3 circles, and so on? In general, how many signs can you make with n circles?

Here are the answers up to n=4 circles (not forgetting n=0):

n Signs consisting of n circles Number
of signs
0 1
1 1
2 2
3 4
4 9

You may like to work out a few more for yourself. In case you do, the results for n=5,6,... etc are not given here, but are to be found on the next page.