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a(n) = determinant of n X n circulant matrix whose first row is the first n square numbers 0, 1, ..., (n-1)^2.
1

%I #7 Mar 16 2017 21:16:57

%S 0,-1,65,-6720,1080750,-252806400,81433562119,-34630270976000,

%T 18813448225370124,-12719917900800000000,10478214213011739186685,

%U -10333870908014534470926336,12023263324381930168836397850,-16297888825404790818315505238016

%N a(n) = determinant of n X n circulant matrix whose first row is the first n square numbers 0, 1, ..., (n-1)^2.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CirculantMatrix.html">Circulant Matrix</a>.

%F a(n) = (-1)^(n-1)*(n-1)*(2*n-1)*n^(n-2)*(n^n-(n-2)^n)/12 [From Missouri State University Problem-Solving Group (MSUPSG(AT)MissouriState.edu), May 05 2010]

%e a(2) = -1 because of the determinant -1 =

%e | 0, 1 |

%e | 1, 0 |.

%e a(3) = 65 = determinant

%e |0,1,4|

%e |4,0,1|

%e |1,4,0|.

%Y See also: A000290 The squares: a(n) = n^2. A048954 Wendt determinant of n-th circulant matrix C(n). A052182 Circulant of natural numbers. A066933 Circulant of prime numbers. A086459 Circulant of powers of 2.

%Y Cf. A000290, A048954, A052182, A066933, A086459, A086569.

%K easy,sign

%O 1,3

%A _Jonathan Vos Post_, May 20 2006

%E More terms from _Alois P. Heinz_, Mar 16 2017