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A134541
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Triangle read by rows: A000012 * A054525 regarded as infinite lower triangular matrices.
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6
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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, 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
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OFFSET
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1,11
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COMMENTS
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Row sums = 1.
Left border = A002321, the Mertens function.
A134541 * [1,2,3,...] = A002088: (1, 2, 4, 6, 10, 12, 18, 22, ...).
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LINKS
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FORMULA
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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
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EXAMPLE
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First few rows of the triangle:
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, 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;
...
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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