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%I #4 Aug 31 2014 14:56:31
%S 1,-63,19548,-16772800,30639466125,-102246541593840,
%T 563353842016350448,-4769009964086911303680,
%U 58776044218330627534385025,-1011412682021947060157500000000,23501115057383512064004090511345788,-717470258224423085595445968714004955136
%N a(n) = determinant of n X n circulant matrix whose first row consists of the first n positive cubes
%F a(n) = (-1)^(n-1)*(n+1)^2*n^(n-2)*(n^(2n)-b(n)^n-c(n)^n+(n^2+3n+3)^n)/24
%F where
%F b(n)=(2*n^2+3*n-3+sqrt(15n^2+18n-9)i)/2 and
%F c(n)=(2*n^2+3*n-3-sqrt(15n^2+18n-9)i)/2
%e a(3) = 19548 = determinant
%e |1, 8, 27|
%e |27, 1, 8|
%e |8, 27, 1|
%t f[n_] := Det[ Table[ RotateLeft[ Range@ n^3, -j], {j, 0, n - 1}]]; Array[f, 12] (* _Robert G. Wilson v_, Aug 31 2014 *)
%Y Cf. A118709
%K easy,sign
%O 1,2
%A Missouri State University Problem-Solving Group (MSUPSG(AT)MissouriState.edu), May 05 2010
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