This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A303832 #19 Dec 02 2020 17:50:03
%S A303832 1,1,4,10,32,101,346,1220,4517,17338,69107,285009,1215015,5344224,
%T A303832 24223641,113001129,541913075,2668817544,13484234188,69831773559,
%U A303832 370361639587,2009988998148,11153858854425,63242354288220,366140089188603,2163036956456422,13031489297543608
%N A303832 The number of edge-rooted unlabeled connected graphs with n edges.
%F A303832 G.f. A(x) satisfies: A(x)*A000664(x) = A126133(x).
%e A303832 a(1)=1: the connected graph with 1 edge (which is rooted).
%e A303832 a(2)=1: the connected graph with 2 edges (one rooted).
%e A303832 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 A303832 (PARI) \\ See A339063 for G.
%o A303832 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 A303832 Cf. A126133 (not necessarily connected), A000664, A303830 (by number of nodes).
%Y A303832 Cf. A002905, A339039, A339040, A339041, A339044.
%K A303832 nonn
%O A303832 1,3
%A A303832 _R. J. Mathar_, May 04 2018