What OEIS sequence is this?

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.

all configurations for N(1), N(2), N(3) are shown here