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

1,2

Links

Table of n, a(n) for n=1..25.

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.

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 *)

Prog

(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)}

Crossrefs

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

Sequence in context: A095940 A018902 A344506 * A363541 A184700 A125586

Adjacent sequences: A339039 A339040 A339041 * A339043 A339044 A339045

Keyword

nonn

Author

Andrew Howroyd, Nov 20 2020

Status

approved