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%I #13 May 06 2018 08:36:59
%S 0,0,1,3,9,27,79,233,679,1987,5784,16864,49063,142821,415439,1208761,
%T 3516475,10232428,29778138,86682119,252382445,735040515,2141319946,
%U 6239913801,18188637903,53033228465,154674931182,451247206423
%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).
%K nonn
%O 1,4
%A _Brendan McKay_, May 05 2018