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Search: id:A137562
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| A137562 |
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Triangular sequence of coefficients from the expansion of p(x,t)=Cos(x*t)/Cos(t). |
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+0
1
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| 1, 0, 1, 0, -1, 0, 5, 0, -6, 0, 1, 0, 61, 0, -75, 0, 15, 0, -1, 0, 1385, 0, -1708, 0, 350, 0, -28, 0, 1, 0, 50521, 0, -62325, 0, 12810, 0, -1050, 0, 45, 0, -1
(list; graph; listen)
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OFFSET
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1,7
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COMMENT
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Row sums are: {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
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FORMULA
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p(x,t)=Cos(x*t)/Cos(t)=Sum[P(x,n)*t^n/n!,{n,0,Infinity}]; out_n,m=n!*Coefficients(p(x,n)).
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EXAMPLE
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{1},
{0},
{1, 0, -1},
{0},
{5, 0, -6, 0, 1},
{0},
{61, 0, -75, 0, 15, 0, -1},
{0},
{1385, 0, -1708, 0, 350, 0, -28, 0, 1},
{0},
{50521, 0, -62325,0, 12810, 0, -1050, 0, 45, 0, -1}
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MATHEMATICA
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p[t_] = Cos[x*t]/Cos[t]; Table[ ExpandAll[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[ CoefficientList[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a] Flatten[{{1}, {0}, {1, 0, -1}, {0}, {5, 0, -6, 0, 1}, {0}, {61, 0, -75, 0, 15, 0, -1}, {0}, {1385, 0, -1708, 0, 350, 0, -28, 0, 1}, {0}, {50521, 0, -62325, 0, 12810, 0, -1050, 0, 45, 0, -1}}]
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CROSSREFS
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Sequence in context: A144702 A055510 A055953 this_sequence A021668 A004552 A130415
Adjacent sequences: A137559 A137560 A137561 this_sequence A137563 A137564 A137565
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KEYWORD
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tabf,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 27 2008
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