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A174841
Determinant of the symmetric n X n matrix M_n where M_n(j,k) = n^abs(j-k).
1
1, -3, 64, -3375, 331776, -52521875, 12230590464, -3938980639167, 1677721600000000, -913517247483640899, 619173642240000000000, -511324276025564512546607, 505488617542763051300683776
OFFSET
1,2
REFERENCES
Jerry Glynn and Theodore Gray, The Beginner's Guide to Mathematica Version 4, Cambridge University Press, 2000, p. 76.
LINKS
FORMULA
a(n) = (1-n^2)^(n-1).
EXAMPLE
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]
MAPLE
for n from 1 to 20 do: x:=(1-n^2)^(n-1):print(x):od:
PROG
(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
CROSSREFS
Sequence in context: A289668 A119924 A231823 * A084883 A304288 A275044
KEYWORD
sign
AUTHOR
Michel Lagneau, Mar 30 2010
EXTENSIONS
Edited by Klaus Brockhaus, Apr 16 2010
STATUS
approved