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A035087
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Number of labeled rooted polygonal cacti (Husimi graphs) with n nodes.
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1
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1, 0, 3, 12, 135, 1440, 20895, 342720, 6585705, 142430400, 3449279295, 92207808000, 2699909867655, 85900402748160, 2951318065570875, 108894519775641600, 4294542443185019025
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listen;
history;
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OFFSET
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1,3
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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.
Harary and E. M. Palmer, Graphical Enumeration, p. 71
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
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LINKS
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Table of n, a(n) for n=1..17.
Index entries for sequences related to cacti
Index entries for sequences related to rooted trees
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FORMULA
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E.g.f. satisfies A(x)=x*exp(A(x)^2/(2-2*A(x))).
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MAPLE
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A:= proc(n) option remember; if n<=1 then x else convert (series (x* exp (A(n-1)^2/ (2-2*A(n-1))), x=0, n+1), polynom) fi end: a:= n-> coeff (A(n), x, n)*n!: seq (a(n), n=1..17); [From Alois P. Heinz, Aug 22 2008]
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CROSSREFS
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Cf. A035082-A035088.
Sequence in context: A073987 A138392 A152544 * A056426 A056417 A098152
Adjacent sequences: A035084 A035085 A035086 * A035088 A035089 A035090
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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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