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Determinant of the n X n matrix whose element (i,j) equals mu(|i-j|) where mu(k) is the moebius function for k > 0 and mu(0) = 0.
2

%I #11 Jan 29 2021 06:56:07

%S 1,0,-1,-2,5,-8,-16,-32,-48,-64,-80,224,-368,312,-205,-2850,5905,

%T 1817592,-4329936,-2004480,-442800,20967000,-349316425,1853293420,

%U -6937330896,24280673168,-18727955840,-31062538500,-42332130415,2736294281648,-27940194392976

%N Determinant of the n X n matrix whose element (i,j) equals mu(|i-j|) where mu(k) is the moebius function for k > 0 and mu(0) = 0.

%H Alois P. Heinz, <a href="/A071085/b071085.txt">Table of n, a(n) for n = 0..500</a>

%p a:= n-> LinearAlgebra[Determinant](Matrix(n, (i, j)->

%p `if`(i=j, 0, numtheory[mobius](abs(i-j))))):

%p seq(a(n), n=0..35); # _Alois P. Heinz_, Jan 28 2021

%t f[n_] := Det[ Table[ MoebiusMu[ Abs[i - j]], {i, 1, n}, {j, 1, n}]]; Table[ f[n], {n, 1, 27}]

%Y Cf. A008683.

%K sign

%O 0,4

%A _Robert G. Wilson v_, May 26 2002

%E a(0)=1 prepended by and more terms from _Alois P. Heinz_, Jan 28 2021