

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
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OFFSET

0,5


COMMENTS

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]


REFERENCES

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and TreeLike Structures, Camb. 1998, p. 301.
F. Harary and R. Z. Norman "The Dissimilarity Characteristic of Husimi Trees" Annals of Mathematics, 58 1953, pp. 134141
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. 315322 1953
Harary, F.; Uhlenbeck, G. (1953), "On the number of Husimi trees, I", Proceedings of the National Academy of Sciences 39: 315322. [From Jonathan Vos Post, Mar 12 2010]


LINKS

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


FORMULA

A035087/n, n>0.


MATHEMATICA

max = 20; s = 1+InverseSeries[Series[E^(x^2/(2*(x1)))*x, {x, 0, max}], x]; a[n_] := SeriesCoefficient[s, n]*(n1)!; a[0]=1; Table[a[n], {n, 0, max}] (* JeanFrançois Alcover, Feb 27 2016, after Vaclav Kotesovec (A035087) *)


CROSSREFS

Cf. A035082A035087.
Sequence in context: A230179 A221769 A065100 * A268094 A013708 A102518
Adjacent sequences: A035085 A035086 A035087 * A035089 A035090 A035091


KEYWORD

nonn,nice


AUTHOR

Christian G. Bower, Nov 15 1998


STATUS

approved



