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A085799
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Determinant of the symmetric n X n matrix A defined by A[i,j] = abs(i^2 - j^2) for 1 <= i,j <= n.
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1
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0, -9, 240, -6300, 181440, -5821200, 207567360, -8172964800, 352864512000, -16593453676800, 844757641728000, -46306798060723200, 2720119606364160000, -170493211041753600000, 11359219476176732160000, -801737767492652390400000, 59762476409805241712640000, -4691769415367001788620800000
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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 * 2^(2*n - 3/2) * n^(n+2) / exp(n).
Recurrence: (14*n - 27)*a(n) = -8*(n-1)*(7*n + 4)*a(n-1) - 36*(2*n - 3)*a(n-2).
(End)
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EXAMPLE
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a(5) = determinant(A) = 181440 where A is the matrix
[ 0 3 8 15 24]
[ 3 0 5 12 21]
[ 8 5 0 7 16]
[15 12 7 0 9]
[24 21 16 9 0] (End)
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MAPLE
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(Conjectured to give the same sequence, apart from signs): a:=n->sum((count(Permutation(n*2-1), size=n+1)), j=0..n)/2: seq(a(n), n=1..16); # Zerinvary Lajos, May 03 2007
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MATHEMATICA
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A[i_, j_] := Abs[i^2 - j^2]; a[n_] := Det[Table[A[i, j], {i, n}, {j, n}]]; Table[a[n], {n, 44}] (* José María Grau Ribas, Apr 17 2010 *)
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PROG
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(Magma) [ Determinant( SymmetricMatrix( &cat[ [ Abs(i^2-j^2): j in [1..i] ]: i in [1..n] ] ) ): n in [1..15] ]; // Klaus Brockhaus, Apr 28 2010
(PARI) a(n) = matdet(matrix(n, n, i, j, abs(i^2-j^2))); \\ Michel Marcus, Aug 14 2017
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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Yuval Dekel (dekelyuval(AT)hotmail.com), Jul 24 2003
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EXTENSIONS
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STATUS
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approved
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