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

1,2

Links

Table of n, a(n) for n=1..26.

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.

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 *)

Prog

(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}

Crossrefs

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

Sequence in context: A150338 A150339 A150340 * A001338 A150341 A150342

Adjacent sequences: A339035 A339036 A339037 * A339039 A339040 A339041

Keyword

nonn

Author

Andrew Howroyd, Nov 20 2020

Status

approved