I've come up with an idea of an integer sequence. It can be formulated (perhaps a bit loosely) as follows: For n points N(n) is the number of configurations where each point either lies on some circle or is a center of some circle. Each point lying on a circle can belong to only 1 circle and each center point can be the center of only 1 circle.
Then N(1) = 2 N(2) = 5 N(3) = 10 N(4) = 20 N(5) = 36 (I double checked N(5) but there is no guarantee that it is the right number)
Depending on how N(0) is defined (N(0)=0 or N(0)=1) this sequence very well can be A000712. However it appears that my description is new, so it easily can be another sequence.