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%I #18 Nov 22 2020 20:23:51
%S 1,2,7,21,66,210,699,2387,8492,31329,120034,477028,1965016,8377888,
%T 36923184,167972182,787688821,3802526173,18873118341,96195592212,
%U 502953711022,2694740822749,14781176429303,82931707378322
%N Number of edge-rooted unlabeled graphs with n edges.
%D F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973.
%H Max Alekseyev, <a href="/A126133/b126133.txt">Table of n, a(n) for n = 1..40</a>
%F G.f.: f(x)*x/(1 + x) where f(x) is the g.f. of A339064. - _Andrew Howroyd_, Nov 22 2020
%e a(3)=7: the triangular graph with one edge rooted. The disconnected graph of the connected linear graph with 3 nodes aside the connected graph with 2 nodes, 2 choices for the root. The three disconnected graphs with 3 graphs on 2 nodes, one of the three with the root. The connected star graph with one edge rooted. The connected linear graph with four nodes, 2 choices for the root. - _R. J. Mathar_, May 03 2018
%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*(1+x)))} \\ _Andrew Howroyd_, Nov 21 2020
%Y Cf. A000664, A126122, A303832 (connected), A339063, A339064.
%K nonn
%O 1,2
%A _Vladeta Jovovic_, Mar 07 2007
%E Terms a(10) onward from _Max Alekseyev_, May 03 2018
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