%I A054365
%S A054365 1,1,1,3,17,102,811,6626,58385,532251,5011934,48344880,475982471,4766639628,
%T A054365 48434621610,498363430232,5184274255789,54451326151253,576810990484823,
%U A054365 6156943228387305,66170786572330174,715564777086617766
%N A054365 Number of unlabeled 5-gonal cacti having n polygons.
%H A054365 Miklos Bona, Michel Bousquet, Gilbert Labelle and Pierre Leroux, Enumeration 
               of m-ary cacti, Advances in Applied Mathematics, 24 (2000), 22-56 
               (<a href="http://www.lacim.uqam.ca/~leroux/articles/cactus.pdf">pdf</
               a>, <a href="http://www.math.ufl.edu/~bona/cactusJCTA.dvi">dvi</a>
               ).
%H A054365 <a href="Sindx_Ca.html#cacti">Index entries for sequences related to 
               cacti</a>
%p A054365 with(combinat): with(numtheory): m := 5: for p from 2 to 28 do s1 := 
               0: s2 := 0: for d from 1 to p do if p mod d = 0 then s1 := s1+phi(p/
               d)*binomial(m*d, d) fi: od: for d from 1 to p-1 do if gcd(m, p-1) 
               mod d = 0 then s2 := s2+phi(d)*binomial((p*m)/d, (p-1)/d) fi: od: 
               printf(`%d, `, (s1+s2)/(m*p)-binomial(m*p, p)/(p*(m-1)+1)) od:
%Y A054365 Sequence in context: A001541 A161940 A074565 this_sequence A116886 A163064 
               A020069
%Y A054365 Adjacent sequences: A054362 A054363 A054364 this_sequence A054366 A054367 
               A054368
%K A054365 nonn
%O A054365 0,4
%A A054365 Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A054365 More terms and Maple program from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Dec 01 2006