A177147 a(n) = determinant of n X n circulant matrix whose first row consists of the first n positive triangular numbers.

1, -8, 190, -8880, 683375, -78206688, 12452171844, -2631354777600, 712425472573815, -240455417915625000, 98981390235327670642, -48810267466347374088192, 28406348214047496113497895, -19264981823338548859573191040, 15061032335471422549306640625000

Offset

1,2

Links

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

Formula

a(n) = (-1)^(n-1)*n^(n-2)*(n+1)*(n+2)*((n+3)^n-(n+1)^n)/(6*2^n).

Example

a(4) = determinant of 4 X 4 matrix
| 1,  3,  6, 10|
|10,  1,  3,  6|
| 6, 10,  1,  3|
| 3,  6, 10,  1|
= -8880.

Mathematica

tri[n_] := n (n + 1)/2; f[n_] := Det[ Table[ RotateLeft[ tri@ Range@ n, -j], {j, 0, n - 1}]]; Array[f, 15] (* or *)
f[n_] := (-1)^n*n^(n - 2)(n + 1)(n + 2)((n + 1)^n - (n + 3)^n)/(3*2^(n + 1)); Array[f, 15]  (* Robert G. Wilson v, Aug 31 2014 *)

Prog

(PARI) A177147(n)={ (-1)^(n-1)*n^(n-2)*(n+1)*(n+2)*((n+3)^n-(n+1)^n)/(6*2^n) ; }
{ for(n=1, 20, print1(A177147(n)", ") ; ) ; } \\ R. J. Mathar, May 28 2010

Crossrefs

Cf. A118705.

Sequence in context: A380648 A272529 A198282 * A366150 A251669 A158654

Adjacent sequences: A177144 A177145 A177146 * A177148 A177149 A177150

Keyword

easy,sign

Author

Missouri State University Problem-Solving Group (MSUPSG(AT)MissouriState.edu), May 03 2010

Extensions

More terms from R. J. Mathar, May 28 2010

Two more terms from Robert G. Wilson v, Aug 31 2014

Status

approved