A091488 - OEIS

%I #12 Aug 30 2018 18:56:44

%S 1,1,1,3,6,16,42,115,319,909,2614,7622,22422,66556,198946,598617,

%T 1811205,5508015,16825307,51605568,158860950,490666293,1520106655,

%U 4722502437,14708971581,45921804883,143682973435,450477673623

%N Number of asymmetric rooted 2,3 cacti (triangular cacti with bridges).

%C Also asymmetric involution rooted trees.

%H Andrew Howroyd, <a href="/A091488/b091488.txt">Table of n, a(n) for n = 1..500</a>

%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 = WEIGH(W_1, 2(a)). W_1, 2(a) has g.f. A(x)+(A(x^2)-A(x)^2)/2.

%o (PARI) WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v,n,(-1)^(n-1)/n))))-1,-#v)}

%o seq(n)={my(p=O(x)); for(n=1, n, p=x+x^2*(Ser(WeighT(Vec(p + (p^2 - subst(p,x,x^2))/2))))); Vec(p)} \\ _Andrew Howroyd_, Aug 30 2018

%Y Cf. A091486, A091489.

%K nonn,eigen

%O 1,4

%A _Christian G. Bower_, Jan 14 2004