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Number of isomorphism classes of non-anti-associative closed binary operations on a set of order n, listed by class size.
6

%I #6 Jul 10 2011 18:42:30

%S 0,2,6,3,10,78,3229,2,1,12,30,246,495,48427,178914959

%N Number of isomorphism classes of non-anti-associative closed binary operations on a set of order n, listed by class size.

%C A079178(n)+A079181(n)=A079171(n).

%C Elements per row: 1,2,4,8,16,30,... (given by A027423, number of positive divisors of n!)

%C First four rows: 0; 2,6; 3,10,78,3229; 2,1,12,30,246,495,48427,178914959

%C A079176(x) is equal to the sum of the products of each element in row x of this sequence and the corresponding element of A079210.

%C The sum of each row x of this sequence is given by A079177(x).

%H C. van den Bosch, <a href="http://cosmos.ucc.ie/~cjvdb1/html/binops.shtml">Closed binary operations on small sets</a>

%H <a href="/index/Gre#groupoids">Index entries for sequences related to groupoids</a>

%Y Cf. A079176, A079177, A079179.

%K nonn,tabf

%O 1,2

%A Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003