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A035086
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Number of increasing rooted polygonal cacti (Husimi graphs) with n nodes.
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0
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1, 0, 1, 3, 19, 135, 1204, 12537, 150556, 2043930, 30969211, 517973148, 9478800604, 188381470095, 4040440921699, 93020386382742, 2287969523647171, 59877222907995675, 1661259526266784171
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Nodes are numbered and the numbers increase as you move away from the root to any point on the same polygon.
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REFERENCES
| F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 301 and Chapter 5.
F. 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
| Index entries for sequences related to cacti
Index entries for sequences related to rooted trees
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FORMULA
| E.g.f. satisfies A'(x)=exp(A(x)^2/(2-2*A(x))).
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MAPLE
| A:= proc(n) option remember; if n<=1 then x else convert (series (Int (exp (A(n-1)^2/ (2-2*A(n-1))), x), x=0, n+1), polynom) fi end; a:= n-> coeff (A(n), x, n)*n!; seq (a(n), n=1..19); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 22 2008]
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CROSSREFS
| Cf. A035082-A035088.
Sequence in context: A063395 A074567 A091346 * A105797 A138513 A094661
Adjacent sequences: A035083 A035084 A035085 * A035087 A035088 A035089
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KEYWORD
| nonn,eigen
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), Nov 15 1998
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