This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A129360 #15 Aug 04 2018 14:27:54
%S A129360 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 A129360 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 A129360 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 A129360 A054525 * A115361.
%C A129360 Row sums = A209229 (1, 1, 0, 1, 0, 0, 0, 1, ...).
%C A129360 A129353 = the inverse Möbius transform of A115361.
%H A129360 Andrew Howroyd, <a href="/A129360/b129360.txt">Table of n, a(n) for n = 1..1275</a>
%F A129360 Moebius transform of A115361.
%F A129360 T(n,k) = A087003(n/k) for k | n, T(n,k) = 0 otherwise. - _Andrew Howroyd_, Aug 03 2018
%e A129360 First few rows of the triangle are:
%e A129360 1;
%e A129360 0, 1;
%e A129360 -1, 0, 1;
%e A129360 0, 0, 0, 1;
%e A129360 -1, 0, 0, 0, 1;
%e A129360 0, -1, 0, 0, 0, 1;
%e A129360 -1, 0, 0, 0, 0, 0, 1;
%e A129360 0, 0, 0, 0, 0, 0, 0, 1;
%e A129360 ...
%o A129360 (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 A129360 (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 A129360 Column 1 is A087003 (Moebius transform of A209229).
%Y A129360 Row sums are A209229.
%Y A129360 Cf. A054525, A115361, A129353, A001511, A103994, A129501.
%K A129360 tabl,sign
%O A129360 1,1
%A A129360 _Gary W. Adamson_, Apr 10 2007
%E A129360 More terms from _Michel Marcus_, Mar 28 2015
%E A129360 Offset changed by _Andrew Howroyd_, Aug 03 2018