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Number of simple connected graphs with n nodes and exactly 1 articulation point (cutpoints).
7

%I #24 Nov 25 2020 05:06:44

%S 0,0,1,2,7,33,244,2792,52448,1690206,96288815,9873721048,

%T 1841360945834,629414405238720,397024508142598996,

%U 464923623652122023478,1016016289424631486429082,4162473006943138723685574978,32096861904411547975392065322659

%N Number of simple connected graphs with n nodes and exactly 1 articulation point (cutpoints).

%C Terms may be computed from A004115. See formula. There is an obvious bijection between a connected graph with 1 articulation point and a multiset of at least two rooted nonseparable graphs joined at the root node. - _Andrew Howroyd_, Nov 24 2020

%H Andrew Howroyd, <a href="/A241767/b241767.txt">Table of n, a(n) for n = 1..26</a>

%H Travis Hoppe and Anna Petrone, <a href="https://github.com/thoppe/Encyclopedia-of-Finite-Graphs">Encyclopedia of Finite Graphs</a>

%H T. Hoppe and A. Petrone, <a href="http://arxiv.org/abs/1408.3644">Integer sequence discovery from small graphs</a>, arXiv preprint arXiv:1408.3644 [math.CO], 2014.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ArticulationVertex.html">Articulation Vertex</a>

%F G.f.: x/(Product_{k>=1} (1 - x^k)^A004115(k+1)) - x - Sum_{k>=1} A004115(k)*x^k. - _Andrew Howroyd_, Nov 24 2020

%Y Column k=1 of A325111.

%Y Cf. other simple connected graph sequences with k articulation points A002218, A241767, A241768, A241769, A241770, A241771.

%Y Cf. A004115 (rooted and without articulation points).

%K nonn

%O 1,4

%A _Travis Hoppe_ and _Anna Petrone_, Apr 28 2014

%E Terms a(11) and beyond from _Andrew Howroyd_, Nov 24 2020