A339037 Number of unlabeled connected loopless multigraphs with n edges rooted at one oriented edge.

1, 3, 11, 41, 160, 641, 2672, 11479, 50938, 232830, 1095151, 5292990, 26257328, 133548307, 695752146, 3709509938, 20224607541, 112675185837, 641016837378, 3721624588590, 22037618432547, 133023405207408, 818085097509494, 5123460267381837, 32660335570381961, 211825198708110059

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 A339065 and g(x) is the g.f. of A050535.

Mathematica

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

Crossrefs

Cf. A050535, A076864, A339036, A339038, A339042, A339043, A339044, A339065.

Sequence in context: A356618 A129637 A084077 * A027103 A151086 A151087

Adjacent sequences: A339034 A339035 A339036 * A339038 A339039 A339040

Keyword

nonn

Author

Andrew Howroyd, Nov 20 2020

Status

approved