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Number of noncrossing 2,3 cacti with n nodes.
7

%I #8 Mar 11 2023 00:13:10

%S 1,1,1,4,20,115,715,4683,31824,222300,1586310,11514030,84742320,

%T 630946446,4743789260,35965715780,274659794160,2110810059795,

%U 16312695488265,126693445737170,988340783454380,7740875273884445,60846920004855985,479854293574853085

%N Number of noncrossing 2,3 cacti with n nodes.

%C A 2,3 cactus is a cactus composed of bridges and triangles.

%H Andrew Howroyd, <a href="/A361245/b361245.txt">Table of n, a(n) for n = 0..500</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Cactus_graph">Cactus graph</a>.

%H <a href="/index/Ca#cacti">Index entries for sequences related to cacti</a>.

%o (PARI) seq(n) = Vec(1 + x/(1 - serreverse((sqrt(1 + 4*x + O(x^n)) - 1)*(1 - x)^2/2)))

%Y Cf. A091481, A091485, A091486, A091487, A361242, A361244.

%K nonn

%O 0,4

%A _Andrew Howroyd_, Mar 08 2023