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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 (list; table; graph; refs; listen; history; text; internal format)
 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 LINKS 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 Adjacent sequences:  A137508 A137509 A137510 * A137512 A137513 A137514 KEYWORD uned,tabl,sign AUTHOR Roger L. Bagula, Apr 23 2008 STATUS approved

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Last modified May 19 13:24 EDT 2022. Contains 353833 sequences. (Running on oeis4.)