A339043 - OEIS

%I #14 Feb 26 2023 14:39:24

%S 1,3,11,43,178,767,3425,15783,74775,363639,1811808,9239430,48175945,

%T 256658465,1396152633,7750325528,43882706171,253308596926,

%U 1490040961732,8928063141435,54469529215562,338236254603888,2136952452531537,13731571816349732,89710429044324926

%N Number of unlabeled connected loopless multigraphs with n edges rooted at two indistinguishable vertices.

%F G.f: f(g) - (g(x)^2 + g(x^2))/2 where x*f(x) is the g.f. of A339038 and g(x) is the g.f. of A339036.

%t seq[n_] := Module[{g, gr}, g = G[2n, x+O[x]^n, {}]; gr = G[2n, x+O[x]^n, {1}]/g; G[2n, x+O[x]^n, {1, 1}]/g - gr^2 + G[2n, x+O[x]^n, {2}]/g - (Normal[gr] /. x -> x^2) // CoefficientList[#/2, x]& // Rest];

%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), g=G(2*n, x+A, []), gr=G(2*n, x+A, [1])/g); Vec(G(2*n, x+A, [1, 1])/g - gr^2 + G(2*n, x+A, [2])/g - subst(gr, x, x^2))/2}

%Y Cf. A050535, A076864, A339036, A339037, A339038, A339041, A339042, A339065.

%K nonn

%O 1,2

%A _Andrew Howroyd_, Nov 20 2020