A137511 - OEIS

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.

-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

Table of n, a(n) for n=1..55.

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