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
KEYWORD
AUTHOR
Roger L. Bagula, Apr 23 2008
STATUS
approved