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Number of non-commutative closed binary operations on a set of order n.
4

%I #12 Jan 28 2013 01:21:24

%S 0,8,18954,4293918720,298023193359375000,

%T 10314424798468598595531571200,

%U 256923577521058877628624940679495660344806,6277101735386680763835789098689112757675628661308013936640

%N Number of non-commutative closed binary operations on a set of order n.

%C A023813(n) + A079182(n) = A002489(n).

%C Each a(n) is equal to the sum of the products of each element in row n of A079184 and the corresponding element of A079210.

%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>

%F a(n) = n^(n^2)-n^((n^2-n)/2).

%t Table[n^(n^2)-n^((n^2+n)/2), {n,1,10}] (* _Geoffrey Critzer_, Jan 27 2013 *)

%Y Cf. A023813, A079178, A079180.

%K nonn

%O 1,2

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

%E More terms from _Geoffrey Critzer_, Jan 27 2013