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%I #21 Feb 09 2024 10:28:07
%S 1,2,11,185,8782,1067825,312510571,212133402500,326266056291213,
%T 1118902054495975181,8455790399687227104576,
%U 139537050182278289405732939,4991058955493997577840793161279
%N Number of essential graphs with n nodes (in 1-1 correspondence with Markov equivalence classes of acyclic digraphs).
%D S. B. Gillispie and M. D. Perlman, Enumerating Markov equivalence classes of acyclic digraph models, Proc. of Conf. on Uncertainty in Artificial Intelligence (2001), 171-177.
%D S. B. Gillispie and M. D. Perlman, The size distribution for Markov equivalence classes of acyclic digraph models, Artificial Intelligence, 141 (2002), 137-155.
%D Bertran Steinsky, Enumeration of Labelled Essential Graphs, Ars Comb., 111, (2013), 485-494
%H S. B. Gillispie and M. D. Perlman, <a href="http://stat.washington.edu/www/research/reports/2001/tr392.pdf">Enumerating Markov equivalence classes of acyclic digraph models</a>, Univ. of Washington, Dept. of Statistics, Technical Reports.
%H S. B. Gillispie and M. D. Perlman, <a href="http://stat.washington.edu/www/research/reports/2001/tr400.pdf">The size distribution for Markov equivalence classes of acyclic digraph models</a>, Univ. of Washington, Dept. of Statistics, Technical Reports.
%Y Cf. A368569 (refined by # arcs).
%K nonn
%O 1,2
%A David Madigan (madigan(AT)stat.washington.edu)
%E More terms from Steven B. Gillispie (gillisp(AT)u.washington.edu), Oct 21 2003
%E a(10) corrected by Steven B. Gillispie (gillisp(AT)u.washington.edu), Aug 14 2007, who says: I have learned from _Bertran Steinsky_ (who determined the correct number) that there was an error in my computer software that computed a(10). The correct value is 1118902054495975181.
%E a(11)-a(13) from _Bertran Steinsky_, Jun 24 2013
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