login
Number of isomorphism classes of non-commutative closed binary operations on a set of order n, listed by class size.
4

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

%S 0,4,2,2,8,70,3121,2,1,14,22,275,467,48306,178888897

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

%C A079184(n)+A079185(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; 4,2; 2,8,70,3121; 2,1,14,22,275,467,48306,178888897

%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 n is given by A079177(n).

%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. A079182, A079183, A079185.

%K nonn,tabf

%O 1,2

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