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A174841
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Determinant of the symmetric n X n matrix M_n where M_n(j,k) = n^abs(j-k).
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1
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1, -3, 64, -3375, 331776, -52521875, 12230590464, -3938980639167, 1677721600000000, -913517247483640899, 619173642240000000000, -511324276025564512546607, 505488617542763051300683776
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OFFSET
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1,2
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REFERENCES
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Jerry Glynn and Theodore Gray, The Beginner's Guide to Mathematica Version 4, Cambridge University Press, 2000, p. 76.
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LINKS
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FORMULA
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a(n) = (1-n^2)^(n-1).
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EXAMPLE
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a(4) = determinant(M_4) = -3375 where M_4 is the matrix
[ 1 4 16 64]
[ 4 1 4 16]
[16 4 1 4]
[64 16 4 1]
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MAPLE
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for n from 1 to 20 do: x:=(1-n^2)^(n-1):print(x):od:
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PROG
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(Magma) [ Determinant( SymmetricMatrix( &cat[ [ n^Abs(j-k): k in [1..j] ]: j in [1..n] ] ) ): n in [1..13] ]; // Klaus Brockhaus, Apr 16 2010
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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