%I A000798 M3631 N1476
%S A000798 1,1,4,29,355,6942,209527,9535241,642779354,63260289423,8977053873043,
%T A000798 1816846038736192,519355571065774021,207881393656668953041,
%U A000798 115617051977054267807460,88736269118586244492485121,93411113411710039565210494095,
               134137950093337880672321868725846,261492535743634374805066126901117203
%N A000798 Number of different quasi-orders (or topologies, or transitive digraphs) 
               with n labeled elements.
%C A000798 a(17)-a(18) are from Brinkmann's and McKay's paper. - Vladeta Jovovic 
               (vladeta(AT)eunet.rs), Jun 10 2007
%D A000798 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000798 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000798 Moussa Benoumhani, The Number of Topologies on a Finite Set, Journal 
               of Integer Sequences, Vol. 9 (2006), Article 06.2.6.
%D A000798 J. I. Brown and S. Watson, The number of complements of a topology on 
               n points is at least 2^n (except for some special cases), Discr. 
               Math., 154 (1996), 27-39.
%D A000798 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 229.
%D A000798 M. Erne' and K. Stege, Counting Finite Posets and Topologies, Order, 
               8 (1991), 247-265.
%D A000798 J. W. Evans, F. Harary and M. S. Lynn, On the computer enumeration of 
               finite topologies, Commun. ACM, 10 (1967), 295-297, 313.
%D A000798 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 
               1973, p. 243.
%D A000798 J. Heitzig and J. Reinhold, The number of unlabeled orders on fourteen 
               elements, Order 17 (2000) no. 4, 333-341.
%D A000798 D. J. Kleitman and B. L. Rothschild, The number of finite topologies, 
               Proc. Amer. Math. Soc., 25 (1970), 276-282.
%D A000798 M. Rayburn, On the Borel fields of a finite set, Proc. Amer. Math.. Soc., 
               19 (1968), 885-889.
%D A000798 A. Shafaat, On the number of topologies definable for a finite set, J. 
               Austral. Math. Soc., 8 (1968), 194-198.
%D A000798 For further references concerning the enumeration of topologies and posets 
               see under A001035.
%H A000798 Gunnar Brinkmann and Brendan D. McKay, <a href="http://cs.anu.edu.au/
               ~bdm/papers/posets.pdf">Posets on up to 16 points</a>.
%H A000798 S. R. Finch, <a href="http://algo.inria.fr/bsolve/">Transitive relations, 
               topologies and partial orders</a>
%H A000798 Institut f. Mathematik, Univ. Hanover, <a href="http://www-ifm.math.uni-hannover.de/
               html/preprints.phtml">Erne/Heitzig/Reinhold papers</a>
%H A000798 G. Pfeiffer, <a href="http://www.cs.uwaterloo.ca/journals/JIS/">Counting 
               Transitive Relations</a>, Journal of Integer Sequences, Vol. 7 (2004), 
               Article 04.3.2.
%H A000798 D. Rusin, <a href="http://www.math.niu.edu/~rusin/known-math/97/finite.top">
               More info and references</a>
%H A000798 N. J. A. Sloane, <a href="classic.html#POSETS">Classic Sequences</a>
%H A000798 <a href="Sindx_Cor.html#core">Index entries for "core" sequences</a>
%F A000798 Related to A000798 by A000798(n) = Sum Stirling2(n, k)*A001035(k).
%Y A000798 Cf. A000798 (labeled topologies), A001035 (labeled posets), A001930 (unlabeled 
               topologies), A000112 (unlabeled posets), A006057.
%Y A000798 Sequence in context: A118795 A099700 A137646 this_sequence A135485 A162287 
               A166168
%Y A000798 Adjacent sequences: A000795 A000796 A000797 this_sequence A000799 A000800 
               A000801
%K A000798 nonn,nice,core,hard
%O A000798 0,3
%A A000798 N. J. A. Sloane (njas(AT)research.att.com).
%E A000798 Two more terms from Jobst Heitzig (heitzig(AT)math.uni-hannover.de), 
               Jul 03 2000