%N Number of trees with n vertices rooted at a non-edge.
%F a(n) + A027852(n) = A303833(n).
%e a(3)=1: the non-edge joins two leaves. a(4)=3: The non-edge joins two leaves of the star graph; or the non-edge joins the two leaves of the linear graph; or the non-edge joins a leaf with the node at distance 2.
%Y Cf. A000055 (not rooted), A027852 (rooted at an edge), A304068 (rooted at an oriented non-edge).
%A _Brendan McKay_, May 05 2018