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A339038
Number of unlabeled connected loopless multigraphs with n edges rooted at one unoriented edge.
5
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
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}
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Nov 20 2020
STATUS
approved