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A137511
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A triangular sequence from coefficients of an expansion of the Poisson's kernel: p(t,r)=(1-r^2)/(1-2*r*Cos(t)+r^2): r->t;Cos(t)->x.
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-1, 0, -2, 4, 0, -8, 0, 36, 0, -48, -48, 0, 384, 0, -384, 0, -1200, 0, 4800, 0, -3840, 1440, 0, -25920, 0, 69120, 0, -46080, 0, 70560, 0, -564480, 0, 1128960, 0, -645120, -80640, 0, 2580480, 0, -12902400, 0, 20643840, 0, -10321920, 0, -6531840, 0, 87091200, 0, -313528320, 0, 418037760, 0, -185794560
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Row sums:
{-1, -2, -4, -12, -48, -240, -1440, -10080, -80640, -725760, -7257600}
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REFERENCES
| Kenneth Hoffman, Banach Spaces of Analytic Functions, Dover, New York, 1962, page30
Thomas McCullough and Keith Phillips, Foundations of Analysis in the Complex Plane, Holt, Reinhart and Winston, New York, 1973, 215
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FORMULA
| p(t,r)=(1-r^2)/(1-2*r*Cos(t)+r^2): r->t;Cos(t)->x. p(t,x)=Sum(p(x,n)&t^n/n!,{n,0,Infinity}]; Out_n,m=n!*Coefficients(P(x,n)).
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EXAMPLE
| {-1},
{0, -2},
{4,0, -8},
{0, 36, 0, -48},
{-48, 0, 384, 0, -384},
{0, -1200, 0, 4800, 0, -3840},
{1440, 0, -25920, 0, 69120, 0, -46080},
{0,70560, 0, -564480, 0, 1128960, 0, -645120},
{-80640, 0, 2580480, 0, -12902400, 0, 20643840, 0, -10321920},
{0, -6531840, 0, 87091200, 0, -313528320, 0, 418037760, 0, -185794560}, {7257600, 0, -362880000, 0, 2903040000, 0, -8128512000, 0, 9289728000, 0, -3715891200}
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MATHEMATICA
| Clear[p, f, g] p[t_] = -(1 - t^2)/(1 - 2*t*x + t^2); Table[ ExpandAll[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[ CoefficientList[n!*SeriesCoefficient[ FullSimplify[Series[p[t], {t, 0, 30}]], n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
| Sequence in context: A076813 A049289 A099890 * A011166 A181274 A115341
Adjacent sequences: A137508 A137509 A137510 * A137512 A137513 A137514
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KEYWORD
| uned,tabl,sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 23 2008
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