A339036 Number of unlabeled connected loopless multigraphs with n edges rooted at one distinguished vertex.

1, 1, 3, 9, 30, 104, 390, 1518, 6208, 26372, 116221, 529341, 2487054, 12027502, 59778867, 304916272, 1594273763, 8535706749, 46753269749, 261771468438, 1497087288210, 8739579074131, 52045067963540, 315980654042243, 1954770128712348, 12315770916526091

Offset: 0

Author

Andrew Howroyd, Nov 20 2020

Keywords

• nonn

Crossrefs

Cf. A007717, A050535, A076864, A339037, A339038, A339039, A339042, A339043, A339065.

Programs

Mathematica

seq[n_] := G[2n, x+O[x]^n, {1}]/G[2n, x+O[x]^n, {}] // CoefficientList[#, x]&;
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)); Vec(G(2*n, x+A, [1])/G(2*n, x+A, []))}

Formula

G.f.: f(x)/g(x) where f(x) is the g.f. of A007717 and g(x) is the g.f. of A050535.