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A143442 Triangle read by rows, A127648 * A000012 * A128407, 1 <= k <= n.

%I A143442 #5 Mar 19 2017 01:04:25
%S A143442 1,2,-2,3,-3,-3,4,-4,-4,0,5,-5,-5,0,-5,6,-6,-6,0,-6,6,7,-7,-7,0,-7,7,
%T A143442 -7,8,-8,-8,0,-8,8,-8,0,9,-9,-9,0,-9,9,-9,0,0,10,-10,-10,0,-10,10,-10,
%U A143442 0,0,10,11,-11,-11,0,-11,11,-11,0,0,11,-11
%N A143442 Triangle read by rows, A127648 * A000012 * A128407, 1 <= k <= n.
%C A143442 Row sums = A143443, n * (A002321, the Mertens function) = (1, 0, -3, -4, -10, -6, ...).
%C A143442 Right border = n*mu(n).
%F A143442 Triangle read by rows, A127648 * A000012 * A128407, 1 <= k <= n; where A127648 = an infinite lower triangular matrix with (1, 2, 3, ...) in the main diagonal, the rest zeros. A128407 = diagonalized mu(n) matrix.
%e A143442 First few rows of the triangle =
%e A143442 1;
%e A143442 2, -2;
%e A143442 3, -3, -3;
%e A143442 4, -4, -4, 0;
%e A143442 5, -5, -5, 0, -5;
%e A143442 6, -6, -6, 0, -6, 6;
%e A143442 7, -7, -7, 0, -7, 7, -7;
%e A143442 ...
%Y A143442 Cf. A002321, A008683, A127648, A128407, A143443.
%K A143442 tabl,sign
%O A143442 1,2
%A A143442 _Gary W. Adamson_, Aug 15 2008