login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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)
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 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]

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*(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) *)

CROSSREFS

Cf. A035082-A035087.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 18 12:00 EDT 2019. Contains 327170 sequences. (Running on oeis4.)