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%I #10 Feb 26 2023 13:42:06
%S 1,3,12,44,171,664,2688,11133,47682,210275,955940,4473128,21532160,
%T 106504216,540824997,2816636171,15031261538,82123830645,458979942506,
%U 2621982351176,15298840540234,91112889589166,553492059017778,3427579611162937,21625096669854023,138927108066308515
%N Number of unlabeled loopless multigraphs with n edges rooted at two indistinguishable vertices.
%e The a(1) = 3 cases correspond to a single edge which can be attached to zero, one or both of the roots.
%t seq[n_] := G[2n, x + O[x]^n, {1, 1}] + G[2n, x + O[x]^n, {2}] // CoefficientList[#/2, x]&;
%t seq[15] (* _Jean-François Alcover_, Dec 02 2020, after _Andrew Howroyd_'s code for G in A339065 *)
%o (PARI) \\ See A339065 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)}
%Y Cf. A050535, A007717 (one root), A339043, A339064, A339065.
%K nonn
%O 0,2
%A _Andrew Howroyd_, Nov 22 2020
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