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A035353
Number of asymmetric rooted polygonal cacti with bridges (mixed Husimi trees).
4
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
0,5
FORMULA
Shifts left under transform T where Ta = WEIGH(BHK(a)).
PROG
(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
KEYWORD
nonn,eigen
AUTHOR
Christian G. Bower, Nov 15 1998
STATUS
approved