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A118705 a(n) = determinant of n X n circulant matrix whose first row is the first n triangular numbers A000217(0), A000217(1), ... A000217(n-1). 1
0, -1, 28, -1360, 105500, -12051585, 1908871832, -400855203840, 107838796034520, -36175347978515625, 14806446317943766420, -7263073394295238840320, 4206546078973080241293076, -2840250692354398785860048105, 2211476237421629752792968750000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..15.

Eric Weisstein's World of Mathematics, Circulant Matrix.

FORMULA

a(n) = (-1)^(n-1)*n^(n-2)*(n+1)*(n-1)*((n+1)^n-(n-1)^n)/(6*2^n) [From Missouri State University Problem-Solving Group (MSUPSG(AT)MissouriState.edu), May 03 2010]

EXAMPLE

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

| 0, 1 |

| 1, 0 |.

a(4) = -1360 = determinant

|0,1,3,6|

|6,0,1,3|

|3,6,0,1|

|1,3,6,0|.

CROSSREFS

See also: 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. A000045, A048954, A052182, A066933, A086459, A086569.

Sequence in context: A281328 A091993 A213692 * A249348 A013926 A110696

Adjacent sequences:  A118702 A118703 A118704 * A118706 A118707 A118708

KEYWORD

easy,sign

AUTHOR

Jonathan Vos Post, May 20 2006

EXTENSIONS

More terms from Alois P. Heinz, Mar 16 2017

STATUS

approved

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Last modified October 18 21:56 EDT 2021. Contains 348070 sequences. (Running on oeis4.)