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A136261
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Triangle T(n,k) = k*A122188(n,k), read by rows.
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0
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-1, -1, 2, 1, 2, -3, -1, -2, -3, 4, 1, 2, 3, 4, -5, -1, -2, -3, -4, -5, 6, 1, 2, 3, 4, 5, 6, -7, -1, -2, -3, -4, -5, -6, -7, 8, 1, 2, 3, 4, 5, 6, 7, 8, -9, -1, -2, -3, -4, -5, -6, -7, -8, -9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -11
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OFFSET
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1,3
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COMMENTS
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Multiplication of the columns of A122188 by their index is equivalent to differentiation of the polynomials B(n,x) defined in A122188.
Row sums are -1, 1, 0, -2, 5, -9, 14, -20, 27, -35, 44, ... =(-1)^n*A080956(n-1).
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LINKS
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FORMULA
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EXAMPLE
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-1;
-1, 2;
1, 2, -3;
-1, -2, -3, 4;
1, 2, 3, 4, -5;
-1, -2, -3, -4, -5, 6;
1, 2, 3, 4, 5, 6, -7;
-1, -2, -3, -4, -5, -6, -7, 8;
1, 2, 3, 4, 5, 6, 7, 8, -9;
-1, -2, -3, -4, -5, -6, -7, -8, -9, 10;
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -11;
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MATHEMATICA
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Clear[B, x, n] B[x, 0] = 1; B[x, 1] = -x + 1; B[x_, n_] := B[x, n] = If[n > 1, (-1)^n*(x^n - Sum[x^m, {m, 0, n - 1}])]; P[x_, n_] := D[B[x, n + 1], x]; Table[ExpandAll[P[x, n]], {n, 0, 10}]; a = Table[CoefficientList[P[x, n], x], {n, 0, 10}]; Flatten[a] Table[Apply[Plus, CoefficientList[P[x, n], x]], {n, 0, 10}];
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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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