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A155124
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Coefficient triangle of polynomial: p(x,m)= -(m - 1) + 2*Sum[x^k, {k, 1, m}].
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1
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1, 0, 2, -1, 2, 2, -2, 2, 2, 2, -3, 2, 2, 2, 2, -4, 2, 2, 2, 2, 2, -5, 2, 2, 2, 2, 2, 2, -6, 2, 2, 2, 2, 2, 2, 2, -7, 2, 2, 2, 2, 2, 2, 2, 2, -8, 2, 2, 2, 2, 2, 2, 2, 2, 2, -9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Row sums are :n;{1,2,3,4,5,6,7,8,9,10,...}
These polynomials in n are column functions for general Pascal-Sierpinki
triangles.
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FORMULA
| p(x,m)= -(m - 1) + 2*Sum[x^k, {k, 1, m}]; t(m,n)=coefficients(p(x,m))
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EXAMPLE
| {1},
{0, 2},
{-1, 2, 2},
{-2, 2, 2, 2},
{-3, 2, 2, 2, 2},
{-4, 2, 2, 2, 2, 2},
{-5, 2, 2, 2, 2, 2, 2},
{-6, 2, 2, 2, 2, 2, 2, 2},
{-7, 2, 2, 2, 2, 2, 2, 2, 2},
{-8, 2, 2, 2, 2, 2, 2, 2, 2, 2},
{-9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2}
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MATHEMATICA
| Clear[f, n, m]; f[n_, m_] = -(m - 1) + 2*Sum[n^k, {k, 1, m}];
Table[ExpandAll[ -(m - 1) + 2*Sum[n^k, {k, 1, m}]], {m, 1, 10}]'
Table[CoefficientList[ExpandAll[ -(m - 1) + 2*Sum[n^ k, {k, 1, m}]], n], {m, 0, 10}];
Flatten[%]
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CROSSREFS
| Sequence in context: A036485 A030547 A156642 * A138033 A067754 A194824
Adjacent sequences: A155121 A155122 A155123 * A155125 A155126 A155127
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KEYWORD
| uned,sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 20 2009
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