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%I #17 Feb 18 2020 19:24:58
%S 1,1,3,11,46,208,1002,5012,25863,136519,733902,4003475,22106155,
%T 123313289,693871975,3933700703,22447035938,128828019447,743142630614,
%U 4306327193744,25056121416684,146325789652514,857393585946194,5039223717251954,29700183601347111,175496470696059267
%N Number of rooted unlabeled 4-cactus graphs on 3n+1 nodes.
%H Andrew Howroyd, <a href="/A287891/b287891.txt">Table of n, a(n) for n = 0..500</a>
%H Maryam Bahrani and Jérémie Lumbroso, <a href="http://arxiv.org/abs/1608.01465">Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition</a>, arXiv:1608.01465 [math.CO], 2016.
%o (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
%o seq(n)={my(v=[]); for(n=1, n, my(g=1+x*Ser(v)); v=EulerT(Vec(g*(g^2 + subst(g, x, x^2))/2))); concat([1], v)} \\ _Andrew Howroyd_, Feb 17 2020
%Y Column k=4 of A332648.
%Y Cf. A003080, A287889, A287890, A287892.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Jun 21 2017
%E a(0) changed and terms a(11) and beyond from _Andrew Howroyd_, Feb 17 2020
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