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A158854
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A triangle of polynomial coefficients: p(x,n)=If[n == 0, 1, (1 - x)^(Floor[(n)/2] + 1)(1 + x)^(Floor[(n - 1)/2])].
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1
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1, 1, -1, 1, -2, 1, 1, -1, -1, 1, 1, -2, 0, 2, -1, 1, -1, -2, 2, 1, -1, 1, -2, -1, 4, -1, -2, 1, 1, -1, -3, 3, 3, -3, -1, 1, 1, -2, -2, 6, 0, -6, 2, 2, -1, 1, -1, -4, 4, 6, -6, -4, 4, 1, -1, 1, -2, -3, 8, 2, -12, 2, 8, -3, -2, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are zero except for n=0.
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FORMULA
| p(x,n)=If[n == 0, 1, (1 - x)^(Floor[(n)/2] + 1)(1 + x)^(Floor[(n - 1)/2])];
t(n,m)=coefficients(p(x,n),x)
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EXAMPLE
| {1},
{1, -1},
{1, -2, 1},
{1, -1, -1, 1},
{1, -2, 0, 2, -1},
{1, -1, -2, 2, 1, -1},
{1, -2, -1, 4, -1, -2, 1},
{1, -1, -3, 3, 3, -3, -1, 1},
{1, -2, -2, 6, 0, -6, 2, 2, -1},
{1, -1, -4, 4, 6, -6, -4, 4, 1, -1},
{1, -2, -3, 8, 2, -12, 2, 8, -3, -2, 1}
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MATHEMATICA
| Clear[p, x, n, m, a];
p[x_, n_] = If[n == 0, 1, (1 - x)^(Floor[(n)/ 2] + 1)(1 + x)^(Floor[(n - 1)/2])];
Table[ExpandAll[p[x, n]], {n, 0, 10}];
Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 0, 10}];
Flatten[%]
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CROSSREFS
| A051160
Sequence in context: A168516 A194321 A194852 * A119849 A026492 A139551
Adjacent sequences: A158851 A158852 A158853 * A158855 A158856 A158857
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KEYWORD
| sign,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 28 2009
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