%I #2 Mar 31 2012 20:25:00
%S 1,-1,2,-1,0,3,0,-2,0,2,-1,0,0,0,5,1,-2,-3,0,0,2,-1,0,0,0,0,0,7,0,0,0,
%T -2,0,0,0,2,0,0,-3,0,0,0,0,0,3,1,-2,0,0,-5,0,0,0,0,2,-1,0,0,0,0,0,0,0,
%U 0,0,11,0,2,0,-2,0,-2,0,0,0,0,0,2,-1,0,0,0,0,0,0,0,0,0,0,0,13,1,-2,0,0,0,0,-7,0,0,0,0,0,0,2
%N Triangle read by rows, A054525 * (A020639 * 0^(n-k)), 1<=k<=n.
%C Right border = A020639, Lpf(n): (1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11,...).
%C Left border = mu(n), A008683: (1, -1, -1, 0, -1, 1, -1,...).
%C Row sums = a signed version of A097945: (1, -1, -2, 0, -4, 2, -6,...) such that parity = (+) iff mu(n) = +.
%F Triangle read by rows, A054525 * (A020639 * 0^(n-k)), 1<=k<=n; where A020639 = Lpf(n): (1, 2, 3, 2, 5, 2, 7, 2, 3, 2,...) and A054525 = the Mobius transform.
%e First few rows of the triangle =
%e 1;
%e -1, 2;
%e -1, 0, 3;
%e 0, -2, 0, 2;
%e -1, 0, 0, 0, 5;
%e 1, -2, -3, 0, 0, 2;
%e -1, 0, 0, 0, 0, 0, 7;
%e 0, 0, 0, -2, 0, 0, 0, 2;
%e 0, 0, -3, 0, 0, 0, 0, 0, 3;
%e 1, -2, 0, 0, -5, 0, 0, 0, 0, 2;
%e -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11;
%e 0, 2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 2;
%e ...
%Y Cf. A008683, A097945, A020639, A054525.
%K tabl,sign
%O 1,3
%A Gary W. Adamson & _Mats Granvik_, Jul 27 2008