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

%I A174841 #12 Sep 08 2022 08:45:51
%S A174841 1,-3,64,-3375,331776,-52521875,12230590464,-3938980639167,
%T A174841 1677721600000000,-913517247483640899,619173642240000000000,
%U A174841 -511324276025564512546607,505488617542763051300683776
%N A174841 Determinant of the symmetric n X n matrix M_n where M_n(j,k) = n^abs(j-k).
%D A174841 Jerry Glynn and Theodore Gray, The Beginner's Guide to Mathematica Version 4, Cambridge University Press, 2000, p. 76.
%H A174841 Vincenzo Librandi, <a href="/A174841/b174841.txt">Table of n, a(n) for n = 1..76</a>
%F A174841 a(n) = (1-n^2)^(n-1).
%e A174841 a(4) = determinant(M_4) = -3375 where M_4 is the matrix
%e A174841 [ 1  4 16 64]
%e A174841 [ 4  1  4 16]
%e A174841 [16  4  1  4]
%e A174841 [64 16  4  1]
%p A174841 for n from 1 to 20 do: x:=(1-n^2)^(n-1):print(x):od:
%o A174841 (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 A174841 Cf. A005249, A067689.
%K A174841 sign
%O A174841 1,2
%A A174841 _Michel Lagneau_, Mar 30 2010
%E A174841 Edited by _Klaus Brockhaus_, Apr 16 2010