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A085799 Determinant of the symmetric n X n matrix A defined by A[i,j] = abs(i^2 - j^2) for 1 <= i,j <= n. 1
0, -9, 240, -6300, 181440, -5821200, 207567360, -8172964800, 352864512000, -16593453676800, 844757641728000, -46306798060723200, 2720119606364160000, -170493211041753600000, 11359219476176732160000, -801737767492652390400000, 59762476409805241712640000, -4691769415367001788620800000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
From Vaclav Kotesovec, Jan 08 2019: (Start)
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)
EXAMPLE
From Klaus Brockhaus, Apr 28 2010: (Start)
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)
MAPLE
(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
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Cf. A085750.
Sequence in context: A279492 A297747 A211052 * A278858 A274789 A263158
KEYWORD
sign
AUTHOR
Yuval Dekel (dekelyuval(AT)hotmail.com), Jul 24 2003
EXTENSIONS
More terms from José María Grau Ribas, Apr 17 2010
Edited by N. J. A. Sloane, Apr 21 2010 at the suggestion of R. J. Mathar
More terms from Michel Marcus, Aug 14 2017
STATUS
approved

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Last modified May 17 19:42 EDT 2024. Contains 372603 sequences. (Running on oeis4.)