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A154853
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Symmetrical triangular sequence: p(x,n) =((-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(3*m + 2)^ n*x^m, {m, 0, Infinity}] - (-1)^(n + 1)*(x - 1)^(n + 1)* Sum[(3*m + 1)^n*x^m, {m, 0, Infinity}].
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1, -1, 3, 0, -3, 7, 33, -33, -7, 15, 294, 0, -294, -15, 31, 1915, 3820, -3820, -1915, -31, 63, 11088, 65115, 0, -65115, -11088, -63, 127, 60725, 783237, 1019935, -1019935, -783237, -60725, -127, 255, 322794, 8095794, 26928930, 0, -26928930, -8095794
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Row sums are are zero.
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FORMULA
| p(x,n) = ((-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(3*m + 2)^ n*x^m, {m, 0, Infinity}]
- (-1)^(n + 1)*(x - 1)^(n + 1)* Sum[(3*m + 1)^n*x^m, {m, 0, Infinity}];
t(n,m)=coefficients(p(x,n))
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EXAMPLE
| {0},
{1, -1},
{3, 0, -3},
{7, 33, -33, -7},
{15, 294, 0, -294, -15},
{31, 1915, 3820, -3820, -1915, -31},
{63, 11088, 65115, 0, -65115, -11088, -63},
{127, 60725, 783237, 1019935, -1019935, -783237, -60725, -127},
{255, 322794, 8095794, 26928930, 0, -26928930, -8095794, -322794, -255},
{511, 1685871, 76977306, 495339306, 498145536, -498145536, -495339306, -76977306, -1685871, -511},
{1023, 8705796, 695435301, 7712761176, 18166178646, 0, -18166178646, -7712761176, -695435301, -8705796, -1023}
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MATHEMATICA
| Clear[p]; p[x_, n_] = ((-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(3*m + 2)^ n*x^m, {m, 0, Infinity}]
- (-1)^(n + 1)*(x - 1)^(n + 1)* Sum[(3*m + 1)^n*x^m, {m, 0, Infinity}];
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: A074694 A127803 A021771 * A139214 A010030 A197270
Adjacent sequences: A154850 A154851 A154852 * A154854 A154855 A154856
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KEYWORD
| tabl,uned,tabl,sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 16 2009
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