cp's OEIS Frontend

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

%I A035088 #22 Sep 06 2023 22:41:36
%S A035088 1,1,0,1,3,27,240,2985,42840,731745,14243040,313570845,7683984000,
%T A035088 207685374435,6135743053440,196754537704725,6805907485977600,
%U A035088 252620143716765825,10015402456976716800,422410127508300756825,18884777200534941696000
%N A035088 Number of labeled polygonal cacti (Husimi graphs) with n nodes.
%C A035088 A Husimi tree is a connected graph in which no line lies on more than one cycle [Harary, 1953]. - _Jonathan Vos Post_, Mar 12 2010
%D A035088 F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 301.
%D A035088 F. Harary and R. Z. Norman "The Dissimilarity Characteristic of Husimi Trees" Annals of Mathematics, 58 1953, pp. 134-141.
%D A035088 F. Harary and E. M. Palmer, Graphical Enumeration, p. 71.
%D A035088 F. Harary and G. E. Uhlenbeck "On the Number of Husimi Trees" Proc. Nat. Acad. Sci. USA vol. 39. pp. 315-322, 1953.
%D A035088 F. Harary, G. Uhlenbeck (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 A035088 Alois P. Heinz, <a href="/A035088/b035088.txt">Table of n, a(n) for n = 0..400</a>
%H A035088 <a href="/index/Ca#cacti">Index entries for sequences related to cacti</a>
%H A035088 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A035088 a(n) = A035087(n)/n, n > 0.
%t A035088 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_ at A035087 *)
%Y A035088 Cf. A035082, A035083, A035084, A035085, A035086, A035087.
%K A035088 nonn,nice
%O A035088 0,5
%A A035088 _Christian G. Bower_, Nov 15 1998