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A143153 Triangle read by rows, A054525 * (A020639 * 0^(n-k)), 1<=k<=n.

%I A143153 #2 Mar 31 2012 20:25:00
%S A143153 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 A143153 -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 A143153 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 A143153 Triangle read by rows, A054525 * (A020639 * 0^(n-k)), 1<=k<=n.
%C A143153 Right border = A020639, Lpf(n): (1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11,...).
%C A143153 Left border = mu(n), A008683: (1, -1, -1, 0, -1, 1, -1,...).
%C A143153 Row sums = a signed version of A097945: (1, -1, -2, 0, -4, 2, -6,...) such that parity = (+) iff mu(n) = +.
%F A143153 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 A143153 First few rows of the triangle =
%e A143153 1;
%e A143153 -1, 2;
%e A143153 -1, 0, 3;
%e A143153 0, -2, 0, 2;
%e A143153 -1, 0, 0, 0, 5;
%e A143153 1, -2, -3, 0, 0, 2;
%e A143153 -1, 0, 0, 0, 0, 0, 7;
%e A143153 0, 0, 0, -2, 0, 0, 0, 2;
%e A143153 0, 0, -3, 0, 0, 0, 0, 0, 3;
%e A143153 1, -2, 0, 0, -5, 0, 0, 0, 0, 2;
%e A143153 -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11;
%e A143153 0, 2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 2;
%e A143153 ...
%Y A143153 Cf. A008683, A097945, A020639, A054525.
%K A143153 tabl,sign
%O A143153 1,3
%A A143153 Gary W. Adamson & _Mats Granvik_, Jul 27 2008