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%I #15 Aug 04 2018 14:27:54
%S 1,0,1,-1,0,1,0,0,0,1,-1,0,0,0,1,0,-1,0,0,0,1,-1,0,0,0,0,0,1,0,0,0,0,
%T 0,0,0,1,0,0,-1,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,
%U 1,0,0,0,-1,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,1
%N A054525 * A115361.
%C Row sums = A209229 (1, 1, 0, 1, 0, 0, 0, 1, ...).
%C A129353 = the inverse Möbius transform of A115361.
%H Andrew Howroyd, <a href="/A129360/b129360.txt">Table of n, a(n) for n = 1..1275</a>
%F Moebius transform of A115361.
%F T(n,k) = A087003(n/k) for k | n, T(n,k) = 0 otherwise. - _Andrew Howroyd_, Aug 03 2018
%e First few rows of the triangle are:
%e 1;
%e 0, 1;
%e -1, 0, 1;
%e 0, 0, 0, 1;
%e -1, 0, 0, 0, 1;
%e 0, -1, 0, 0, 0, 1;
%e -1, 0, 0, 0, 0, 0, 1;
%e 0, 0, 0, 0, 0, 0, 0, 1;
%e ...
%o (PARI) tabl(nn) = {Tm = matrix(nn, nn, n, k, if (! (n % k), moebius(n/k), 0)); Tr = matrix(nn, nn, n, k, n--; k--; if ((n==k), 1, if (n==2*k+1, -1, 0))); Ti = Tr^(-1); Tp = Tm*Ti; for (n=1, nn, for (k=1, n, print1(Tp[n, k], ", ");); print(););} \\ _Michel Marcus_, Mar 28 2015
%o (PARI) T(n, k)={ if(n%k, 0, sumdiv(n/k, d, my(e=valuation(d, 2)); if(d==1<<e, moebius(n/(k*d)), 0))) } \\ _Andrew Howroyd_, Aug 03 2018
%Y Column 1 is A087003 (Moebius transform of A209229).
%Y Row sums are A209229.
%Y Cf. A054525, A115361, A129353, A001511, A103994, A129501.
%K tabl,sign
%O 1,1
%A _Gary W. Adamson_, Apr 10 2007
%E More terms from _Michel Marcus_, Mar 28 2015
%E Offset changed by _Andrew Howroyd_, Aug 03 2018
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