# 20 circles in the plane, all passing through the origin

Suppose I draw $$2020$$ circles in the plane, all passing through the origin, but no two tangent at the origin. Also, except for the origin, no three circles pass through a common point. How many regions are created in the plane?

Move the origin to $\infty$ using the map $z\mapsto{1\over z}$. Then the circles become lines, no two of them parallel, and no three of them going through the same point.
Denote the number of regions created by $n$ lines by $a_n$, and find a recursion for the $a_n$.