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
Examples
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.
Crossrefs
Cf. A118705.
Programs
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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 *) -
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
Formula
a(n) = (-1)^(n-1)*n^(n-2)*(n+1)*(n+2)*((n+3)^n-(n+1)^n)/(6*2^n).
Extensions
More terms from R. J. Mathar, May 28 2010
Two more terms from Robert G. Wilson v, Aug 31 2014