A339043 Number of unlabeled connected loopless multigraphs with n edges rooted at two indistinguishable vertices.

1, 3, 11, 43, 178, 767, 3425, 15783, 74775, 363639, 1811808, 9239430, 48175945, 256658465, 1396152633, 7750325528, 43882706171, 253308596926, 1490040961732, 8928063141435, 54469529215562, 338236254603888, 2136952452531537, 13731571816349732, 89710429044324926

Offset

1,2

Links

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

Formula

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.

Mathematica

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];
seq[15] (* Jean-François Alcover, Dec 02 2020, after 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, []), 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}

Crossrefs

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

Sequence in context: A151092 A151093 A151094 * A103821 A151095 A219262

Adjacent sequences: A339040 A339041 A339042 * A339044 A339045 A339046

Keyword

nonn

Author

Andrew Howroyd, Nov 20 2020

Status

approved