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A035082
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Number of rooted polygonal cacti (Husimi graphs) with n nodes.
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19
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0, 1, 0, 1, 1, 3, 5, 13, 27, 67, 157, 390, 963, 2437, 6186, 15908, 41127, 107148, 280569, 738675, 1953054, 5185364, 13816018, 36934431, 99030038, 266254593, 717652816, 1938831589, 5249221790, 14240130827, 38702218134, 105367669062
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refs;
listen;
history;
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internal format)
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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.
F. Harary and E. M. Palmer, Graphical Enumeration, p. 71
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 0..500
C. G. Bower, Transforms (2)
F. Harary and R. Z. Norman, The Dissimilarity Characteristic of Husimi Trees, Annals of Mathematics, 58 1953, pp. 134-141.
F. Harary and G. E. Uhlenbeck, On the Number of Husimi Trees, Proc. Nat. Acad. Sci. USA vol. 39 pp. 315-322 1953
N. J. A. Sloane, Transforms
Index entries for sequences related to cacti
Index entries for sequences related to rooted trees
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FORMULA
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Shifts left under transform T where Ta = EULER(BIK(a)-a).
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PROG
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(PARI)
BIK(p)={(1/(1-p) + (1+p)/subst(1-p, x, x^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)))); concat([0], Vec(p))} \\ Andrew Howroyd, Aug 30 2018
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CROSSREFS
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Cf. A003080, A035083, A035084, A035085, A035086, A035087, A035088.
Sequence in context: A190570 A000631 A026569 * A005198 A160823 A077443
Adjacent sequences: A035079 A035080 A035081 * A035083 A035084 A035085
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KEYWORD
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nonn,eigen
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AUTHOR
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Christian G. Bower, Nov 15 1998
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STATUS
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approved
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