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%I #22 Aug 30 2018 18:56:01
%S 1,1,2,3,7,16,41,106,304,880,2674,8284,26347,85076,279324,928043,
%T 3118915,10580145,36199094,124774041,432990333,1511628113,5306305978,
%U 18719781786,66342222729,236100395649,843490024052,3024220006717,10878908844745,39255047915513
%N Number of unlabeled 2,3 cacti (triangular cacti with bridges).
%H Alois P. Heinz, <a href="/A091487/b091487.txt">Table of n, a(n) for n = 1..1000</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.
%H <a href="/index/Ca#cacti">Index entries for sequences related to cacti</a>
%F G.f.: A(x) = B(x)-B(x)^2/2+B(x^2)/2+B(x^3)/3-B(x)^3/3 where B is g.f. of A091486.
%o (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
%o b(n)={my(p=O(x)); for(n=1, n, p=x+x^2*(Ser(EulerT(Vec(p + (p^2 + subst(p,x,x^2))/2))))); p}
%o seq(n)={my(p=b(n)); Vec(p - p^2/2 - p^3/3 + subst(p, x, x^2)/2 + subst(p, x, x^3)/3)} \\ _Andrew Howroyd_, Aug 30 2018
%Y Cf. A091486, A091489.
%K nonn
%O 1,3
%A _Christian G. Bower_, Jan 14 2004
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