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%I M2072 #30 Mar 24 2023 18:05:30
%S 1,1,1,2,14,546,169444,560043206
%N Number of comparative probability orderings on n elements.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Andrew Beveridge, Ian Calaway, and Kristin Heysse, <a href="https://arxiv.org/abs/1912.12319">de Finetti Lattices and Magog Triangles</a>, arXiv:1912.12319 [math.CO], 2019.
%H T. Fine and J. Gill, <a href="https://doi.org/10.1214/aop/1176996036">The enumeration of comparative probability relations</a>, Ann. Prob. 4 (1976) 667-673.
%H D. Maclagan, <a href="https://arxiv.org/abs/math/9809134">Boolean Term Orders and the Root System B_n</a>, arXiv:math/9809134 [math.CO], 1998-1999.
%H D. Maclagan, <a href="https://doi.org/10.1023/A:1006207716298">Boolean Term Orders and the Root System B_n</a>, Order 15 (1999), 279-295.
%F a(n) >= A009997(n) with equality iff n < 5. - _M. F. Hasler_, Mar 17 2023
%e For n = 3, the two orders are 1 < 2 < 12 < 3 < 13 < 23 < 123 and 1 < 2 < 3 < 12 < 13 < 23 < 123.
%e For zero elements, there is exactly one ordering. - _M. F. Hasler_, Mar 17 2023
%Y Cf. A009997.
%K nonn,nice,hard,more
%O 0,4
%A _N. J. A. Sloane_
%E a(7) from Diane Maclagan and _Michael Kleber_
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