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%I #12 Mar 29 2023 17:39:33
%S 1,1,-1,1,0,-1,1,-1,0,0,1,0,0,0,-1,1,-1,-1,0,0,1,1,0,0,0,0,0,-1,1,-1,
%T 0,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,1,-1,0,0,-1,0,0,0,0,1,1,0,0,0,0,0,0,0,
%U 0,0,-1,1,-1,-1,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1
%N Triangle T(n,k): T(n,k) = mu(k) if k divides n, T(n,k)=0 otherwise (n >= 1, 1<=k<=n).
%F A054524 = A051731 * A128407 - _Gary W. Adamson_, Mar 02 2007
%t Clear[t]; t[n_, 1] = 1; t[n_, k_] := t[n, k] = If[k == 1, 1, If[n == k, -Sum[t[n, k - i], {i, 1, k - 1}], If[n > k, t[n - k, k], 0]]]; Flatten[Table[t[n, k], {n, 13}, {k, n}]] (* Mats Granvik, Feb 12 2012 *)
%t Table[If[Mod[n,k]==0,MoebiusMu[k],0],{n,20},{k,n}]//Flatten (* _Harvey P. Dale_, Mar 29 2023 *)
%Y Cf. A054521.
%Y Cf. A051731, A128407.
%K sign,tabl
%O 1,1
%A _N. J. A. Sloane_, Apr 09 2000
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