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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 Vincenzo Librandi, Table of n, a(n) for n = 1..140 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 Adjacent sequences: A085796 A085797 A085798 * A085800 A085801 A085802 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.)