%I
%S 1,1,4,10,32,101,346,1220,4517,17338,69107,285009,1215015,5344224,
%T 24223641,113001129,541913075,2668817544,13484234188,69831773559,
%U 370361639587,2009988998148,11153858854425,63242354288220,366140089188603,2163036956456422,13031489297543608
%N The number of edgerooted unlabeled connected graphs with n edges.
%F G.f. A(x) satisfies: A(x)*A000664(x) = A126133(x).
%e a(1)=1: the connected graph with 1 edge (which is rooted).
%e a(2)=1: the connected graph with 2 edges (one rooted).
%e a(3)=4: the triangle graph with one choice of rooting, the linear tree with either the middle or a terminating edge rooted, the star graph with one edge rooted.
%o (PARI) \\ See A339063 for G.
%o seq(n)={my(A=O(x*x^n)); Vec((G(2*n, x+A, [1, 1]) + G(2*n, x+A, [2]))/(2*G(2*n, x+A, [])*(1+x)))} \\ _Andrew Howroyd_, Nov 21 2020
%Y Cf. A126133 (not necessarily connected), A000664, A303830 (by number of nodes).
%Y Cf. A002905, A339039, A339040, A339041, A339044.
%K nonn
%O 1,3
%A _R. J. Mathar_, May 04 2018
