|
%I #15 Feb 26 2023 13:41:51
%S 1,4,17,73,319,1423,6499,30374,145302,711177,3559690,18212192,
%T 95193547,508083746,2767835600,15382476029,87177582535,503610832756,
%U 2964300557548,17771210411578,108471258414870,673836620069035,4258727230198033,27373904651169023,178885471934461869
%N Number of unlabeled connected loopless multigraphs with n edges rooted at two noninterchangeable vertices.
%F G.f.: f(x) - g(x)^2 where x*f(x) is the g.f. of A339037 and g(x) is the g.f. of A339036.
%t seq[n_] := Module[{g}, g = G[2n, x+O[x]^n, {}]; G[2n, x+O[x]^n, {1, 1}]/g - (G[2n, x+O[x]^n, {1}]/g)^2 // CoefficientList[#, x]& // Rest];
%t seq[15] (* _Jean-François Alcover_, Dec 02 2020, using _Andrew Howroyd_'s code for G in A339065 *)
%o (PARI) \\ See A339065 for G.
%o seq(n)={my(A=O(x*x^n), g=G(2*n, x+A, [])); Vec(G(2*n, x+A, [1, 1])/g - (G(2*n, x+A, [1])/g)^2)}
%Y Cf. A050535, A076864, A339036, A339037, A339038, A339040, A339043, A339065.
%K nonn
%O 1,2
%A _Andrew Howroyd_, Nov 20 2020
|
