cp's OEIS Frontend

A035353 Number of asymmetric rooted polygonal cacti with bridges (mixed Husimi trees).

%I A035353 #15 Aug 30 2018 18:57:10
%S A035353 0,1,1,1,3,7,22,67,215,692,2283,7599,25631,87211,299386,1035059,
%T A035353 3602083,12606318,44344764,156698081,555989604,1980050697,7075365521,
%U A035353 25360341963,91155701023,328500571740,1186656421109,4296084607302
%N A035353 Number of asymmetric rooted polygonal cacti with bridges (mixed Husimi trees).
%H A035353 Andrew Howroyd, <a href="/A035353/b035353.txt">Table of n, a(n) for n = 0..200</a>
%H A035353 C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%H A035353 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A035353 <a href="/index/Ca#cacti">Index entries for sequences related to cacti</a>
%H A035353 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%H A035353 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A035353 Shifts left under transform T where Ta = WEIGH(BHK(a)).
%o A035353 (PARI)
%o A035353 BHK(p)={p + (1/(1-p) - (1+p)/subst(1-p, x, x^2))/2}
%o A035353 WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v,n,(-1)^(n-1)/n))))-1,-#v)}
%o A035353 seq(n)={my(v=[0]); for(n=1, n, v=concat([0,1], WeighT(Vec(BHK(Ser(v)))))); v} \\ _Andrew Howroyd_, Aug 30 2018
%Y A035353 Cf. A000083, A000237, A000314, A035082, A035349-A035357.
%K A035353 nonn,eigen
%O A035353 0,5
%A A035353 _Christian G. Bower_, Nov 15 1998