A174841 Determinant of the symmetric n X n matrix M_n where M_n(j,k) = n^abs(j-k).

1, -3, 64, -3375, 331776, -52521875, 12230590464, -3938980639167, 1677721600000000, -913517247483640899, 619173642240000000000, -511324276025564512546607, 505488617542763051300683776

Offset: 1

Author

Michel Lagneau, Mar 30 2010

Keywords

• sign

Examples

			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]
		

References

• Jerry Glynn and Theodore Gray, The Beginner's Guide to Mathematica Version 4, Cambridge University Press, 2000, p. 76.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..76

Crossrefs

Cf. A005249, A067689.

Programs

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

Maple

for n from 1 to 20 do: x:=(1-n^2)^(n-1):print(x):od:

Formula

a(n) = (1-n^2)^(n-1).

Extensions

Edited by Klaus Brockhaus, Apr 16 2010