A174841 - OEIS

A174841

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

%I #12 Sep 08 2022 08:45:51

%S 1,-3,64,-3375,331776,-52521875,12230590464,-3938980639167,

%T 1677721600000000,-913517247483640899,619173642240000000000,

%U -511324276025564512546607,505488617542763051300683776

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

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

%H Vincenzo Librandi, <a href="/A174841/b174841.txt">Table of n, a(n) for n = 1..76</a>

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

%e a(4) = determinant(M_4) = -3375 where M_4 is the matrix

%e [ 1 4 16 64]

%e [ 4 1 4 16]

%e [16 4 1 4]

%e [64 16 4 1]

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

%o (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

%Y Cf. A005249, A067689.

%K sign

%O 1,2

%A _Michel Lagneau_, Mar 30 2010

%E Edited by _Klaus Brockhaus_, Apr 16 2010