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A156578
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Coefficients of polynomials: p(x,n)=(1 - x)^2*Sum[(k + 1)*x^k, {k, 0, n - 1}].
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0
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0, 1, -2, 1, 1, 0, -3, 2, 1, 0, 0, -4, 3, 1, 0, 0, 0, -5, 4, 1, 0, 0, 0, 0, -6, 5, 1, 0, 0, 0, 0, 0, -7, 6, 1, 0, 0, 0, 0, 0, 0, -8, 7, 1, 0, 0, 0, 0, 0, 0, 0, -9, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, -10, 9, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 10
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Row sums are all zero.
Based on Identity:
1/(1-x)^2=Sum[(k + 1)*x^k, {k, 0, Infinity}];
broken into parts of the (1-x)^2
and the count up polynomials:
q(x,n)= Sum[(k + 1)*(x)^k, {k, 0, n - 1}].
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FORMULA
| p(x,n)=(1 - x)^2*Sum[(k + 1)*x^k, {k, 0, n - 1}];
t(n,m)=coefficients(p(x,n)).
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EXAMPLE
| {0},
{1, -2, 1},
{1, 0, -3, 2},
{1, 0, 0, -4, 3},
{1, 0, 0, 0, -5, 4},
{1, 0, 0, 0, 0, -6, 5},
{1, 0, 0, 0, 0, 0, -7, 6},
{1, 0, 0, 0, 0, 0, 0, -8, 7},
{1, 0, 0, 0, 0, 0, 0, 0, -9, 8},
{1, 0, 0, 0, 0, 0, 0, 0, 0, -10, 9},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 10}
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MATHEMATICA
| Clear[p];
p[x_, n_] := (1 - x)^2*Sum[(k + 1)*x^k, {k, 0, n - 1}];
Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}];
Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];
Flatten[%]
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CROSSREFS
| Sequence in context: A029352 A055168 A085144 * A171846 A097230 A144789
Adjacent sequences: A156575 A156576 A156577 * A156579 A156580 A156581
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KEYWORD
| sign,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 10 2009
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