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A154852
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Symmetrical triangular sequence: p(x,n) = ((-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(2*m - 1)^n*x^m, {m, 0, Infinity}] - (-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(2*m + 3)^n*x^m, {m, 0, Infinity}])/4.
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0
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-1, 1, -2, 0, 2, -7, -3, 3, 7, -20, -56, 0, 56, 20, -61, -415, -370, 370, 415, 61, -182, -2632, -5710, 0, 5710, 2632, 182, -547, -15155, -64407, -49735, 49735, 64407, 15155, 547, -1640, -82896, -619696, -1085840, 0, 1085840, 619696, 82896, 1640
(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[(2*m - 1)^ n*x^m, {m, 0, Infinity}]
- (-1)^(n + 1)*(x - 1)^(n + 1)* Sum[(2*m + 3)^n*x^m, {m, 0, Infinity}])/4;
t(n,m)=coefficients(p(x,n))
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EXAMPLE
| {0},
{-1, 1},
{-2, 0, 2},
{-7, -3, 3, 7},
{-20, -56, 0, 56, 20},
{-61, -415, -370, 370, 415, 61},
{-182, -2632, -5710, 0, 5710, 2632, 182},
{-547, -15155, -64407, -49735, 49735, 64407, 15155, 547},
{-1640, -82896, -619696, -1085840, 0, 1085840, 619696, 82896, 1640},
{-4921, -439071, -5422116, -16914156, -11926446, 11926446, 16914156, 5422116, 439071, 4921},
{-14762, -2279024, -44560494, -224451744, -337197924, 0, 337197924, 224451744, 44560494, 2279024, 14762}
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MATHEMATICA
| Clear[p]; p[x_, n_] = ((-1)^( n + 1)*(x - 1)^(n + 1)*Sum[(2*m - 1)^n*x^m, {m, 0, Infinity}]
- (-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(2*m + 3)^n*x^m, {m, 0, Infinity}])/4;
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: A111111 A185343 A161014 * A088996 A021497 A201735
Adjacent sequences: A154849 A154850 A154851 * A154853 A154854 A154855
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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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