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%I #7 Nov 17 2013 20:20:21
%S 1,0,0,-5,6,-16,9,-134400,647248,-1711908,6076067,-85248000,116477425,
%T -1764364437,909276004,-522319050599375232,14313181351994538493,
%U -165893335414907083200,2939566160282258664451,-5007637771411479278976,75399747694572065660672
%N a(n) = Determinant of n X n circulant matrix whose first row is A000001(1), A000001(2), ..., A000001(n) where A000001(n) = number of groups of order n.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CirculantMatrix.html">Circulant Matrix</a>.
%e a(4) = -5 because of the determinant -5 =
%e |1,1,1,2|
%e |2,1,1,1|
%e |1,2,1,1|
%e |1,1,2,1|.
%e a(11) = 6076067 = determinant
%e |1, 1, 1, 2, 1, 2, 1, 5, 2, 2, 1|
%e |1, 1, 1, 1, 2, 1, 2, 1, 5, 2, 2|
%e |2, 1, 1, 1, 1, 2, 1, 2, 1, 5, 2|
%e |2, 2, 1, 1, 1, 1, 2, 1, 2, 1, 5|
%e |5, 2, 2, 1, 1, 1, 1, 2, 1, 2, 1|
%e |1, 5, 2, 2, 1, 1, 1, 1, 2, 1, 2|
%e |2, 1, 5, 2, 2, 1, 1, 1, 1, 2, 1|
%e |1, 2, 1, 5, 2, 2, 1, 1, 1, 1, 2|
%e |2, 1, 2, 1, 5, 2, 2, 1, 1, 1, 1|
%e |1, 2, 1, 2, 1, 5, 2, 2, 1, 1, 1|
%e |1, 1, 2, 1, 2, 1, 5, 2, 2, 1, 1|.
%o (GAP) A118712 := n -> DeterminantMat(List([0..n-1], i->List([0..n-1], j->NrSmallGroups(((j-i) mod n)+1)))); # _Eric M. Schmidt_, Nov 17 2013
%Y Cf. A000001, A048954, A052182, A066933, A086459, A086569.
%K sign
%O 1,4
%A _Jonathan Vos Post_, May 20 2006
%E a(1) corrected by and more terms from _Eric M. Schmidt_, Nov 17 2013
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