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%I #12 Mar 15 2015 21:22:59
%S 1,-8,190,-8880,683375,-78206688,12452171844,-2631354777600,
%T 712425472573815,-240455417915625000,98981390235327670642,
%U -48810267466347374088192,28406348214047496113497895,-19264981823338548859573191040,15061032335471422549306640625000
%N a(n) = determinant of n X n circulant matrix whose first row consists of the first n positive triangular numbers.
%F a(n) = (-1)^(n-1)*n^(n-2)*(n+1)*(n+2)*((n+3)^n-(n+1)^n)/(6*2^n).
%e a(4) = determinant of 4 X 4 matrix
%e | 1, 3, 6, 10|
%e |10, 1, 3, 6|
%e | 6, 10, 1, 3|
%e | 3, 6, 10, 1|
%e = -8880.
%t tri[n_] := n (n + 1)/2; f[n_] := Det[ Table[ RotateLeft[ tri@ Range@ n, -j], {j, 0, n - 1}]]; Array[f, 15] (* or *)
%t 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 *)
%o (PARI) A177147(n)={ (-1)^(n-1)*n^(n-2)*(n+1)*(n+2)*((n+3)^n-(n+1)^n)/(6*2^n) ; }
%o { for(n=1,20, print1(A177147(n)",") ; ) ; } \\ _R. J. Mathar_, May 28 2010
%Y Cf. A118705.
%K easy,sign
%O 1,2
%A Missouri State University Problem-Solving Group (MSUPSG(AT)MissouriState.edu), May 03 2010
%E More terms from _R. J. Mathar_, May 28 2010
%E Two more terms from _Robert G. Wilson v_, Aug 31 2014
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