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

0, 1, 1, 1, 3, 7, 22, 67, 215, 692, 2283, 7599, 25631, 87211, 299386, 1035059, 3602083, 12606318, 44344764, 156698081, 555989604, 1980050697, 7075365521, 25360341963, 91155701023, 328500571740, 1186656421109, 4296084607302

Offset: 0

Author

Christian G. Bower, Nov 15 1998

Keywords

• nonn
• eigen

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• C. G. Bower, Transforms (2)
• N. J. A. Sloane, Transforms
• Index entries for sequences related to cacti
• Index entries for sequences related to rooted trees
• Index entries for sequences related to trees

Crossrefs

Cf. A000083, A000237, A000314, A035082, A035349-A035357.

Programs

PARI

BHK(p)={p + (1/(1-p) - (1+p)/subst(1-p, x, x^2))/2}
WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v,n,(-1)^(n-1)/n))))-1,-#v)}
seq(n)={my(v=[0]); for(n=1, n, v=concat([0,1], WeighT(Vec(BHK(Ser(v)))))); v} \\ Andrew Howroyd, Aug 30 2018

Formula

Shifts left under transform T where Ta = WEIGH(BHK(a)).