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A137511
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.
0
-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
OFFSET
1,3
COMMENTS
Row sums:
{-1, -2, -4, -12, -48, -240, -1440, -10080, -80640, -725760, -7257600}
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
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)).
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}
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]
CROSSREFS
Sequence in context: A258053 A099890 A208745 * A011166 A181274 A115341
KEYWORD
uned,tabl,sign
AUTHOR
Roger L. Bagula, Apr 23 2008
STATUS
approved