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 A127514 #12 Feb 15 2022 20:55:12
%S A127514 1,1,-1,1,-2,-1,1,-3,-3,0,1,-4,-6,0,-1,1,-5,-10,0,-5,1,1,-6,-15,0,-15,
%T A127514 6,-1,1,-7,-21,0,-35,21,-7,0,1,-8,-28,0,-70,56,-28,0,0,1,-9,-36,0,
%U A127514 -126,126,-84,0,0,1,1,-10,-45,0,-210,252,-210,0,0,10,-1
%N A127514 Binomial transform of an infinite lower triangular matrix with mu(n) in the diagonal.
%C A127514 Right border = mu(n).
%C A127514 Row sums = A104688, the binomial transform of mu(n): 1, 0, -2, -5, -10, -18, ...
%F A127514 P * M, as infinite lower triangular matrices. P = Pascal's triangle, M = mu(n) in the main diagonal and the rest zeros.
%e A127514 First few rows of the triangle:
%e A127514 1;
%e A127514 1, -1;
%e A127514 1, -2, -1;
%e A127514 1, -3, -3, 0;
%e A127514 1, -4, -6, 0, -1;
%e A127514 1, -5, -10, 0, -5, 1;
%e A127514 ...
%o A127514 (PARI) row(n) = {my(M = matrix(n, n, i, j, if (i==j, moebius(i))), P = matrix(n, n, i, j, binomial(i-1, j-1))); vector(n, k, (P*M)[n, k]);} \\ _Michel Marcus_, Feb 15 2022
%Y A127514 Cf. A007318, A008683, A104688.
%Y A127514 Cf. A127512 (M*P).
%K A127514 sign,tabl
%O A127514 1,5
%A A127514 _Gary W. Adamson_, Jan 17 2007
%E A127514 More terms from _Michel Marcus_, Feb 15 2022