A339038 Number of unlabeled connected loopless multigraphs with n edges rooted at one unoriented edge.

1, 2, 7, 23, 88, 339, 1396, 5915, 26080, 118539, 555678, 2678458, 13262193, 67353325, 350493424, 1866989802, 10171394388, 56631507822, 322011612423, 1868702977253, 11061267210030, 66745602611831, 410360493588788, 2569318971123439, 16374787277199728, 106180292431149021

Offset: 1

Author

Andrew Howroyd, Nov 20 2020

Keywords

• nonn

Crossrefs

Cf. A050535, A076864, A303832, A339036, A339037, A339042, A339043, A339065, A339066.

Programs

Mathematica

seq[n_] := (G[2n, x + O[x]^n, {1, 1}] + G[2n, x + O[x]^n, {2}])/G[2n, x + O[x]^n, {}] // CoefficientList[#/2, x]&;
seq[15] (* Jean-François Alcover, Dec 02 2020, after 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, [1,1]) + G(2*n, x+A, [2]))/G(2*n, x+A, []))/2}

Formula

G.f.: x*f(x)/g(x) where f(x) is the g.f. of A339066 and g(x) is the g.f. of A050535.