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Search: id:A136261
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| A136261 |
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Differentiating A122188: the coefficients of count down polynomials found by differentiating the Bonacci polynomials. |
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+0
1
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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
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Row sums are:
{-1, 1, 0, -2, 5, -9, 14, -20, 27, -35, 44}
In the absolute value, this sequence also computes A002260.
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FORMULA
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b(n,x)=(-1)^n*(x^n - Sum[x^m, {m, 0, n - 1}]); p(x,n)=db(x,n+1)/dx
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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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Cf. A002260, A122188, A107335, A129080.
Sequence in context: A113126 A138060 A023121 this_sequence A140756 A002260 A133994
Adjacent sequences: A136258 A136259 A136260 this_sequence A136262 A136263 A136264
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KEYWORD
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nonn,uned,tabl
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AUTHOR
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Roger L. Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Mar 18 2008
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