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A303832 The number of edge-rooted unlabeled connected graphs with n edges. 6


%S 1,1,4,10,32,101,346,1220,4517,17338,69107,285009,1215015,5344224,

%T 24223641,113001129,541913075,2668817544,13484234188,69831773559,

%U 370361639587,2009988998148,11153858854425,63242354288220,366140089188603,2163036956456422,13031489297543608

%N The number of edge-rooted unlabeled connected graphs with n edges.

%F G.f. A(x) satisfies: A(x)*A000664(x) = A126133(x).

%e a(1)=1: the connected graph with 1 edge (which is rooted).

%e a(2)=1: the connected graph with 2 edges (one rooted).

%e a(3)=4: the triangle graph with one choice of rooting, the linear tree with either the middle or a terminating edge rooted, the star graph with one edge rooted.

%o (PARI) \\ See A339063 for G.

%o seq(n)={my(A=O(x*x^n)); Vec((G(2*n, x+A, [1, 1]) + G(2*n, x+A, [2]))/(2*G(2*n, x+A, [])*(1+x)))} \\ _Andrew Howroyd_, Nov 21 2020

%Y Cf. A126133 (not necessarily connected), A000664, A303830 (by number of nodes).

%Y Cf. A002905, A339039, A339040, A339041, A339044.

%K nonn

%O 1,3

%A _R. J. Mathar_, May 04 2018

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Last modified April 14 15:18 EDT 2021. Contains 342949 sequences. (Running on oeis4.)