|
%I #22 Aug 30 2018 18:55:14
%S 1,1,3,7,21,60,190,600,1977,6589,22408,77050,268178,941599,3333585,
%T 11882427,42615480,153653039,556664752,2025330509,7397242875,
%U 27111563026,99681629658,367563272278,1358945378906,5036549490009,18708739990129,69640873691941
%N Number of unlabeled rooted 2,3 cacti (triangular cacti with bridges).
%C Also number of unlabeled involution rooted trees.
%H Alois P. Heinz, <a href="/A091486/b091486.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 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Ca#cacti">Index entries for sequences related to cacti</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F Shifts left under transform T where Ta = EULER(E_1, 2(a)). E_1, 2(a) has g.f. A(x)+(A(x^2)+A(x)^2)/2.
%o (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
%o seq(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))))); Vec(p)} \\ _Andrew Howroyd_, Aug 30 2018
%Y Cf. A091487, A091488.
%K nonn,eigen
%O 1,3
%A _Christian G. Bower_, Jan 14 2004
|
