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%I #6 Mar 30 2012 18:40:36
%S 1,2,3,8,43,1454,1131985,12199587820,2697830531268481,
%T 15224736759268778589978,2750892227033887206264514123491
%N Number of quasigroups of order <= n.
%C A quasigroup is a groupoid G such that for all a and b in G, there exist unique c and d in G such that ac = b and da = b. Hence a quasigroup is not required to have an identity element, nor be associative. Equivalently, one can state that quasigroups are precisely groupoids whose multiplication tables are Latin squares (possibly empty).
%H <a href="/index/Qua#quasigroups">Index entries for sequences related to quasigroups</a>.
%F a(n) = SUM[i=0..n] A057991(i).
%e a(10) = 2750892227033887206264514123491 = 1 + 1 + 1 + 5 + 35 + 1411 + 1130531 + 12198455835 + 2697818331680661 + 15224734061438247321497 + 2750892211809150446995735533513.
%Y Cf. A002860, A057991-A057994, A057771, A057996, A118641.
%K nonn
%O 1,2
%A _Jonathan Vos Post_, May 12 2006
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