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A035085
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Number of polygonal cacti (Husimi graphs) with n nodes.
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7
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1, 1, 0, 1, 1, 2, 2, 5, 7, 16, 28, 63, 131, 301, 673, 1600, 3773, 9158, 22319, 55255, 137563, 345930, 874736, 2227371, 5700069, 14664077, 37888336, 98310195, 256037795, 669184336, 1754609183, 4614527680
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OFFSET
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0,6
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REFERENCES
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F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 301.
F. Harary and E. M. Palmer, Graphical Enumeration, p. 71.
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LINKS
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FORMULA
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PROG
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(PARI)
BIK(p)={(1/(1-p) + (1+p)/subst(1-p, x, x^2))/2}
DIK(p, n)={(sum(d=1, n, eulerphi(d)/d*log(subst(1/(1+O(x*x^(n\d))-p), x, x^d))) + ((1+p)^2/(1-subst(p, x, x^2))-1)/2)/2}
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
seq(n)={my(p=O(x)); for(n=1, n, p=x+x^2*Ser(EulerT(Vec(BIK(p)-1)-Vec(p)))); Vec(1 + DIK(p, n) - (p^2 + subst(p, x, x^2))/2 - p*(BIK(p)-1-p))} \\ Andrew Howroyd, Aug 31 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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