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A035088 Number of labeled polygonal cacti (Husimi graphs) with n nodes. 4


%S 1,1,0,1,3,27,240,2985,42840,731745,14243040,313570845,7683984000,

%T 207685374435,6135743053440,196754537704725,6805907485977600,

%U 252620143716765825,10015402456976716800,422410127508300756825,18884777200534941696000

%N Number of labeled polygonal cacti (Husimi graphs) with n nodes.

%C 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]

%D F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 301.

%D F. Harary and R. Z. Norman "The Dissimilarity Characteristic of Husimi Trees" Annals of Mathematics, 58 1953, pp. 134-141

%D F. Harary and E. M. Palmer, Graphical Enumeration, p. 71

%D F. Harary and G. E. Uhlenbeck "On the Number of Husimi Trees" Proc. Nat. Acad. Sci. USA vol. 39 pp. 315-322 1953

%D 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]

%H Alois P. Heinz, <a href="/A035088/b035088.txt">Table of n, a(n) for n = 0..400</a>

%H <a href="/index/Ca#cacti">Index entries for sequences related to cacti</a>

%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>

%F A035087/n, n>0.

%t 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) *)

%Y Cf. A035082-A035087.

%K nonn,nice

%O 0,5

%A _Christian G. Bower_, Nov 15 1998

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Last modified October 17 11:47 EDT 2019. Contains 328108 sequences. (Running on oeis4.)