%I A127448
%S A127448 1,1,2,1,0,3,0,2,0,4,1,0,0,0,5,1,2,3,0,0,6,1,0,0,0,0,0,7,0,0,0,4,0,0,0,
%T A127448 8,0,0,3,0,0,0,0,0,9,1,2,0,0,5,0,0,0,0,10,1,0,0,0,0,0,0,0,0,0,11,0,2,
%U A127448 0,4,0,6,0,0,0,0,0,12,1,0,0,0,0,0,0,0,0,0,0,0,13,1,2,0,0,0,0,7,0,0,0,0,
               0,0
%V A127448 1,-1,2,-1,0,3,0,-2,0,4,-1,0,0,0,5,1,-2,-3,0,0,6,-1,0,0,0,0,0,7,0,0,0,
               -4,0,0,0,
%W A127448 8,0,0,-3,0,0,0,0,0,9,1,-2,0,0,-5,0,0,0,0,10,-1,0,0,0,0,0,0,0,0,0,11,0,
               2,
%X A127448 0,-4,0,-6,0,0,0,0,0,12,-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
%N A127448 Triangle T(n,k) read by rows: matrix product A054525 * A127648.
%F A127448 T(n,k) = sum _{j=k..n} A054525(n,j)*A127648(j,k) = k*A054525(n,k).
%F A127448 sum_{k=1..n} T(n,k) = A000010(n) (row sums).
%F A127448 T(n,1) = A008683(n).
%e A127448 First few rows of the triangle are;
%e A127448 1;
%e A127448 -1, 2;
%e A127448 -1, 0, 3;
%e A127448 0, -2, 0, 4;
%e A127448 -1, 0, 0, 0, 5;
%e A127448 1, -2, -3, 0, 0, 6;
%e A127448 -1, 0, 0, 0, 0, 0, 7;
%e A127448 0, 0, 0, -4, 0, 0, 0, 8;
%e A127448 0, 0, -3, 0, 0, 0, 0, 0, 9;
%e A127448 1, -2, 0, 0, 5, 0, 0, 0, 0, 10;
%e A127448 ...
%p A127448 A127648 := proc(n,k) if n = k then n; else 0 ; fi; end:
%p A127448 A054525 := proc(n,k) if k = n then 1; elif n mod k = 0 then numtheory[mobius](n/
               k) ; else 0 ; fi; end:
%p A127448 A127448 := proc(n,k) add( A054525(n,j)*A127648(j,k) , j=k..n) ; end: 
               seq(seq( A127448(n,k),k=1..n),n=1..15) ;
%Y A127448 Cf. A000010, A008683, A051731.
%Y A127448 Sequence in context: A050464 A014405 A143153 this_sequence A128179 A058558 
               A123973
%Y A127448 Adjacent sequences: A127445 A127446 A127447 this_sequence A127449 A127450 
               A127451
%K A127448 tabl,sign,easy
%O A127448 1,3
%A A127448 Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 14 2007
%E A127448 Converted comments to formulas, extended - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Sep 11 2009
%E A127448 Corrected A-number typo in a formula - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Sep 17 2009