A339042 Number of unlabeled connected loopless multigraphs with n edges rooted at two noninterchangeable vertices.

1, 4, 17, 73, 319, 1423, 6499, 30374, 145302, 711177, 3559690, 18212192, 95193547, 508083746, 2767835600, 15382476029, 87177582535, 503610832756, 2964300557548, 17771210411578, 108471258414870, 673836620069035, 4258727230198033, 27373904651169023, 178885471934461869

Offset: 1

Author

Andrew Howroyd, Nov 20 2020

Keywords

• nonn

Crossrefs

Cf. A050535, A076864, A339036, A339037, A339038, A339040, A339043, A339065.

Programs

Mathematica

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];
seq[15] (* Jean-François Alcover, Dec 02 2020, using Andrew Howroyd's code for G in A339065 *)

PARI

\\ See A339065 for G.
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)}

Formula

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.