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

0, -1, 65, -6720, 1080750, -252806400, 81433562119, -34630270976000, 18813448225370124, -12719917900800000000, 10478214213011739186685, -10333870908014534470926336, 12023263324381930168836397850, -16297888825404790818315505238016

Offset: 1

Author

Jonathan Vos Post, May 20 2006

Keywords

• easy
• sign

Examples

			a(2) = -1 because of the determinant -1 =
| 0, 1 |
| 1, 0 |.
a(3) = 65 = determinant
|0,1,4|
|4,0,1|
|1,4,0|.
		

Links

• Eric Weisstein's World of Mathematics, Circulant Matrix.

Crossrefs

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.

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

Formula

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]

Extensions

More terms from Alois P. Heinz, Mar 16 2017