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A177233
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a(n) = determinant of n X n circulant matrix whose first row consists of the first n positive cubes
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0
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1, -63, 19548, -16772800, 30639466125, -102246541593840, 563353842016350448, -4769009964086911303680, 58776044218330627534385025, -1011412682021947060157500000000, 23501115057383512064004090511345788, -717470258224423085595445968714004955136
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OFFSET
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1,2
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LINKS
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FORMULA
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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
where
b(n)=(2*n^2+3*n-3+sqrt(15n^2+18n-9)i)/2 and
c(n)=(2*n^2+3*n-3-sqrt(15n^2+18n-9)i)/2
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EXAMPLE
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a(3) = 19548 = determinant
|1, 8, 27|
|27, 1, 8|
|8, 27, 1|
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MATHEMATICA
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f[n_] := Det[ Table[ RotateLeft[ Range@ n^3, -j], {j, 0, n - 1}]]; Array[f, 12] (* Robert G. Wilson v, Aug 31 2014 *)
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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Missouri State University Problem-Solving Group (MSUPSG(AT)MissouriState.edu), May 05 2010
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STATUS
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approved
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