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A035088
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Number of labeled polygonal cacti (Husimi graphs) with n nodes.
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4
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1, 1, 0, 1, 3, 27, 240, 2985, 42840, 731745, 14243040, 313570845, 7683984000, 207685374435, 6135743053440, 196754537704725, 6805907485977600, 252620143716765825, 10015402456976716800, 422410127508300756825, 18884777200534941696000
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listen;
history;
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OFFSET
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0,5
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COMMENTS
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A Husimi tree is a connected graph in which no line lies on more than one cycle [Harary, 1953]. [From Jonathan Vos Post, Mar 12 2010]
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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 R. Z. Norman "The Dissimilarity Characteristic of Husimi Trees" Annals of Mathematics, 58 1953, pp. 134-141
F. Harary and E. M. Palmer, Graphical Enumeration, p. 71
F. Harary and G. E. Uhlenbeck "On the Number of Husimi Trees" Proc. Nat. Acad. Sci. USA vol. 39 pp. 315-322 1953
Harary, F.; Uhlenbeck, G. (1953), "On the number of Husimi trees, I", Proceedings of the National Academy of Sciences 39: 315-322. [From Jonathan Vos Post, Mar 12 2010]
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..400
Index entries for sequences related to cacti
Index entries for sequences related to trees
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FORMULA
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A035087/n, n>0.
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MATHEMATICA
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max = 20; s = 1+InverseSeries[Series[E^(x^2/(2*(x-1)))*x, {x, 0, max}], x]; a[n_] := SeriesCoefficient[s, n]*(n-1)!; a[0]=1; Table[a[n], {n, 0, max}] (* Jean-François Alcover, Feb 27 2016, after Vaclav Kotesovec (A035087) *)
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CROSSREFS
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Cf. A035082-A035087.
Sequence in context: A230179 A221769 A065100 * A344724 A268094 A013708
Adjacent sequences: A035085 A035086 A035087 * A035089 A035090 A035091
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KEYWORD
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nonn,nice
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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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