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%I A001423 M3550 N1438
%S A001423 1,1,4,18,126,1160,15973,836021,1843120128
%N A001423 Number of semigroups of order n, considered to be equivalent when they 
               are isomorphic or anti-isomorphic (by reversal of the operator).
%D A001423 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001423 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001423 Andreas Distler and Tom Kelsey, The Monoids of Order Eight and Nine, 
               in Intelligent Computer Mathematics, Lecture Notes in Computer Science, 
               Volume 5144/2008, Springer-Verlag. [From N. J. A. Sloane, Jul 10 
               2009]
%D A001423 G. E. Forsythe, SWAC computes 126 distinct semigroups of order 4, Proc. 
               Amer. Math. Soc. 6, (1955). 443-447.
%D A001423 H. Juergensen and P. Wick, Die Halbgruppen von Ordnungen <= 7, Semigroup 
               Forum, 14 (1977), 69-79.
%D A001423 D. J. Kleitman, B. L. Rothschild and J. H. Spencer, The number of semigroups 
               of order n, Proc. Amer. Math. Soc., 55 (1976), 227-232.
%D A001423 R. J. Plemmons, There are 15973 semigroups of order 6, Math. Algor., 
               2 (1967), 2-17; 3 (1968), 23.
%D A001423 Satoh, S.; Yama, K.; and Tokizawa, M., Semigroups of order 8, Semigroup 
               Forum 49 (1994), 7-29.
%H A001423 Eric Postpischil <a href="http://groups.google.com/groups?&hl=en&lr=&ie=UTF-8&selm=11802%40shlump.nac.dec.com\
               &rnum=2">Posting to sci.math newsgroup, May 21 1990</a>
%H A001423 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Semigroup.html">Link to a section of The World of Mathematics.</a>
%H A001423 <a href="Sindx_Se.html#semigroups">Index entries for sequences related 
               to semigroups</a>
%Y A001423 a(n)=(A027851(n)+A029851(n))/2. Cf. A001426, A023814, A058107, A058123, 
               A151823.
%Y A001423 Sequence in context: A112294 A073511 A108704 this_sequence A158341 A144272 
               A034517
%Y A001423 Adjacent sequences: A001420 A001421 A001422 this_sequence A001424 A001425 
               A001426
%K A001423 nonn,hard,nice
%O A001423 0,3
%A A001423 N. J. A. Sloane (njas(AT)research.att.com).

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