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A035088 Number of labeled polygonal cacti (Husimi graphs) with n nodes. 4
1, 1, 0, 1, 3, 27, 240, 2985, 42840, 731745, 14243040, 313570845, 7683984000, 207685374435, 6135743053440, 196754537704725, 6805907485977600, 252620143716765825, 10015402456976716800, 422410127508300756825, 18884777200534941696000 (list; graph; refs; listen; history; text; internal format)



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]


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]


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


A035087/n, n>0.


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-Fran├žois Alcover, Feb 27 2016, after Vaclav Kotesovec (A035087) *)


Cf. A035082-A035087.

Sequence in context: A230179 A221769 A065100 * A268094 A013708 A102518

Adjacent sequences:  A035085 A035086 A035087 * A035089 A035090 A035091




Christian G. Bower, Nov 15 1998



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Last modified December 15 20:00 EST 2019. Contains 330000 sequences. (Running on oeis4.)