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 A134541 #27 Jun 09 2024 09:04:37
%S A134541 1,0,1,-1,1,1,-1,0,1,1,-2,0,1,1,1,-1,-1,0,1,1,1,-2,-1,0,1,1,1,1,-2,-1,
%T A134541 0,0,1,1,1,1,-2,-1,-1,0,1,1,1,1,1,-1,-2,-1,0,0,1,1,1,1,1,-2,-2,-1,0,0,
%U A134541 1,1,1,1,1,1,-2,-1,-1,-1,0,0,1,1,1,1,1,1
%N A134541 Triangle read by rows: A000012 * A054525 regarded as infinite lower triangular matrices.
%C A134541 Row sums = 1.
%C A134541 Left border = A002321, the Mertens function.
%C A134541 A134541 * [1,2,3,...] = A002088: (1, 2, 4, 6, 10, 12, 18, 22, ...).
%F A134541 Recurrence: T(n, k) = If n >= k then If k = 1 then 1 - Sum_{i=1..n-1} T(n, k + i)/(i + 1)^(s - 1) else T(floor(n/k) else 1)) else 0). - _Mats Granvik_, Apr 17 2016
%e A134541 First few rows of the triangle:
%e A134541 1;
%e A134541 0, 1;
%e A134541 -1, 1, 1;
%e A134541 -1, 0, 1, 1;
%e A134541 -2, 0, 1, 1, 1;
%e A134541 -1, -1, 0, 1, 1, 1;
%e A134541 -2, -1, 0, 1, 1, 1, 1;
%e A134541 -2, -1, 0, 0, 1, 1, 1, 1;
%e A134541 -2, -1, -1, 0, 1, 1, 1, 1, 1;
%e A134541 -1, -2, -1, 0, 0, 1, 1, 1, 1, 1;
%e A134541 ...
%t A134541 Clear[t, s, n, k, z, x]; z = 1; nn = 10; t[n_, k_] := t[n, k] = If[n >= k, If[k == 1, 1 - Sum[t[n, k + i]/(i + 1)^(s - 1), {i, 1, n - 1}], t[Floor[n/k], 1]], 0]; Flatten[Table[Table[Limit[t[n, k], s -> z], {k, 1, n}], {n, 1, nn}]] (* _Mats Granvik_, Jul 22 2012 *) (* updated _Mats Granvik_, Apr 10 2016 *)
%Y A134541 Cf. A000012, A054525, A002321, A002088, A134541.
%Y A134541 Matrix inverse of A176702. - _Mats Granvik_, Apr 24 2010
%K A134541 tabl,sign
%O A134541 1,11
%A A134541 _Gary W. Adamson_, Oct 31 2007
%E A134541 More terms from _Amiram Eldar_, Jun 09 2024