A177233 a(n) = determinant of n X n circulant matrix whose first row consists of the first n positive cubes

1, -63, 19548, -16772800, 30639466125, -102246541593840, 563353842016350448, -4769009964086911303680, 58776044218330627534385025, -1011412682021947060157500000000, 23501115057383512064004090511345788, -717470258224423085595445968714004955136

Offset

1,2

Links

Table of n, a(n) for n=1..12.

Formula

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

Example

a(3) = 19548 = determinant
|1, 8, 27|
|27, 1, 8|
|8, 27, 1|

Mathematica

f[n_] := Det[ Table[ RotateLeft[ Range@ n^3, -j], {j, 0, n - 1}]]; Array[f, 12] (* Robert G. Wilson v, Aug 31 2014 *)

Crossrefs

Cf. A118709

Sequence in context: A132594 A212932 A349902 * A183482 A327416 A001238

Adjacent sequences: A177230 A177231 A177232 * A177234 A177235 A177236

Keyword

easy,sign

Author

Missouri State University Problem-Solving Group (MSUPSG(AT)MissouriState.edu), May 05 2010

Status

approved