%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