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A058123 Triangle read by rows: semigroups of order n with k idempotents, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).

%I A058123 #24 Nov 08 2018 14:40:22
%S A058123 1,2,2,5,7,6,19,37,44,26,132,216,351,326,135,3107,1780,3093,4157,2961,
%T A058123 875,623615,32652,33445,53145,56020,30395,6749,1834861133,4665709,
%U A058123 600027,754315,1007475,822176,348692,60601,52976551026562,12710266442,68769167,14050493,18660074,20044250,12889961,4389418,618111
%N A058123 Triangle read by rows: semigroups of order n with k idempotents, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).
%H A058123 Andrey Zabolotskiy, <a href="/A058123/b058123.txt">Table of n, a(n) for n = 1..55</a> (rows 1-10)
%H A058123 Andreas Distler, <a href="http://hdl.handle.net/10023/945">Classification and Enumeration of Finite Semigroups</a>, A Thesis Submitted for the Degree of PhD, University of St Andrews (2010).
%H A058123 Andreas Distler, Chris Jefferson, Tom Kelsey, Lars Kotthoff, <a href="https://doi.org/10.1007/978-3-642-33558-7_63">The Semigroups of Order 10</a>, in: M. Milano (Ed.), Principles and Practice of Constraint Programming, 18th International Conference, CP 2012, Québec City, QC, Canada, October 8-12, 2012, Proceedings (LNCS, volume 7514), pp. 883-899, Springer-Verlag Berlin Heidelberg 2012.
%H A058123 A. Distler and T. Kelsey, <a href="http://arxiv.org/abs/1301.6023">The semigroups of order 9 and their automorphism groups</a>, arXiv preprint arXiv:1301.6023 [math.CO], 2013.
%H A058123 <a href="/index/Se#semigroups">Index entries for sequences related to semigroups</a>
%e A058123 Triangle starts:
%e A058123     1;
%e A058123     2,   2;
%e A058123     5,   7,   6;
%e A058123    19,  37,  44,  26;
%e A058123   132, 216, 351, 326, 135;
%e A058123   ...
%Y A058123 Row sums give A001423. Main diagonal: A002788. Columns 1-3: A002786, A002787, A005591.
%K A058123 nonn,tabl,hard
%O A058123 1,2
%A A058123 _Christian G. Bower_, Nov 10 2000
%E A058123 More terms from _Andreas Distler_, Jan 13 2011