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A177147
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a(n) = determinant of n X n circulant matrix whose first row consists of the first n positive triangular numbers.
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1
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1, -8, 190, -8880, 683375, -78206688, 12452171844, -2631354777600, 712425472573815, -240455417915625000, 98981390235327670642, -48810267466347374088192, 28406348214047496113497895, -19264981823338548859573191040, 15061032335471422549306640625000
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = (-1)^(n-1)*n^(n-2)*(n+1)*(n+2)*((n+3)^n-(n+1)^n)/(6*2^n).
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(PARI) A177147(n)={ (-1)^(n-1)*n^(n-2)*(n+1)*(n+2)*((n+3)^n-(n+1)^n)/(6*2^n) ; }
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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Missouri State University Problem-Solving Group (MSUPSG(AT)MissouriState.edu), May 03 2010
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EXTENSIONS
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STATUS
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approved
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