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%I #3 Mar 30 2012 17:34:27
%S 1,-2,-1,-3,0,-1,0,0,0,0,-5,0,0,0,-1,6,3,2,0,0,1,-7,0,0,0,0,0,-1,0,0,
%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,10,5,0,0,2,0,0,0,0,1,-11,0,0,0,0,0,0,0,
%U 0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,-13,0,0,0,0,0,0,0,0,0,0,0,-1,14,7,0,0,0,0,2,0,0,0,0,0,0,1
%N Triangle read by rows, A128407 * A126988; 1<=k<=n.
%C Left border = A055615: (1, -2, -3, 0, -5, 6, -7,...).
%C Right border = A008683, mu(n).
%C Row sums = A063441: (1, -3, -4, 0, -6, 12, 8,...).
%F Triangle read by rows, A128407 * A126988; 1<=k<=n
%F t(n,m)=MoebiusMu[n]*A126988(n,m); t(n,m)=MoebiusMu[n]*If[m == 1, n, If[Mod[n, m] == 0, n/m, 0]]. - _Roger L. Bagula_, Sep 06 2008
%e First few rows of the triangle =
%e 1;
%e -2, -1;
%e -3, 0, -1;
%e 0, 0, 0, 0;
%e -5, 0, 0, 0, -1;
%e 6, 3, 2, 0, 0, 1;
%e -7, 0, 0, 0, 0, 0, -1;
%e 0, 0, 0, 0, 0, 0, 0, 0;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e 10, 5, 0, 0, 2, 0, 0, 0, 0, 1;
%e ...
%t t[n_, m_] = MoebiusMu[n]*If[m == 1, n, If[Mod[n, m] == 0, n/m, 0]]; Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%] - _Roger L. Bagula_, Sep 06 2008
%Y Cf. A008683, A063441, A055615, A128407, A126988.
%Y Cf. A128988.
%K tabl,sign
%O 1,2
%A _Gary W. Adamson_, Aug 02 2008
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