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A118707 a(n) = determinant of n X n circulant matrix whose first row is the first n square numbers 0, 1, ..., (n-1)^2.

%I A118707 #8 Feb 16 2025 08:33:01
%S A118707 0,-1,65,-6720,1080750,-252806400,81433562119,-34630270976000,
%T A118707 18813448225370124,-12719917900800000000,10478214213011739186685,
%U A118707 -10333870908014534470926336,12023263324381930168836397850,-16297888825404790818315505238016
%N A118707 a(n) = determinant of n X n circulant matrix whose first row is the first n square numbers 0, 1, ..., (n-1)^2.
%H A118707 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CirculantMatrix.html">Circulant Matrix</a>.
%F A118707 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 A118707 a(2) = -1 because of the determinant -1 =
%e A118707 | 0, 1 |
%e A118707 | 1, 0 |.
%e A118707 a(3) = 65 = determinant
%e A118707 |0,1,4|
%e A118707 |4,0,1|
%e A118707 |1,4,0|.
%Y A118707 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 A118707 Cf. A000290, A048954, A052182, A066933, A086459, A086569.
%K A118707 easy,sign
%O A118707 1,3
%A A118707 _Jonathan Vos Post_, May 20 2006
%E A118707 More terms from _Alois P. Heinz_, Mar 16 2017