%I A003080 M1448
%S A003080 1,1,2,5,13,37,111,345,1105,3624,12099,41000,140647,487440,1704115,
%T A003080 6002600,21282235,75890812,272000538,979310627,3540297130,12845634348,
%U A003080 46764904745,170767429511,625314778963,2295635155206,8447553316546
%N A003080 Number of rooted triangular cacti with 2n+1 nodes (n triangles).
%D A003080 F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like 
               Structures, Camb. 1998, p. 305, (4.2.34).
%D A003080 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 
               1973, p. 73, (3.4.20).
%D A003080 P. Leroux and B. Miloudi, ``G\'{e}n\'{e}ralisations de la formule d'Otter,
               '' Ann. Sci. Math. Qu\'{e}bec, Vol. 16, No. 1, pp. 53-80, 1992.
%D A003080 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A003080 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%H A003080 <a href="Sindx_Ca.html#cacti">Index entries for sequences related to 
               cacti</a>
%F A003080 a(n)=b(2n+1). b shifts left under transform T where Tb = EULER(E_2(b)). 
               E_2(b) has g.f. (B(x^2)+B(x)^2)/2.
%Y A003080 Cf. A003081, A034940, A034941.
%Y A003080 Sequence in context: A126031 A151416 A114509 this_sequence A149854 A151442 
               A053732
%Y A003080 Adjacent sequences: A003077 A003078 A003079 this_sequence A003081 A003082 
               A003083
%K A003080 nonn,eigen,nice
%O A003080 0,3
%A A003080 N. J. A. Sloane (njas(AT)research.att.com).
%E A003080 Sequence extended by Paul Zimmermann, Mar 15 1996. Additional comments 
               from Christian G. Bower (bowerc(AT)usa.net).