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Expansion of x/(1 - 22 x^2 - 54 x^3 - 38 x^4).
0

%I #11 Jul 31 2015 20:38:00

%S 0,1,0,22,54,522,2376,15236,82512,483332,2728296,15667920,89257896,

%T 510388840,2913416640,16643861824,95047963488,542884234608,

%U 3100533567552,17708509939040,101139309767520,577645632221792

%N Expansion of x/(1 - 22 x^2 - 54 x^3 - 38 x^4).

%D R. G. Newton, Scattering Theory of Waves and Particles, McGraw Hill, New York, 1966, pp. 557ff.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 22, 54, 38).

%F a(0)=0, a(1)=1, a(2)=0, a(3)=22, a(n)=22*a(n-2)+54*a(n-3)+38*a(n-4) [From Harvey P. Dale, Aug 12 2011]

%t f[x_] = -38 - 54 x - 22 x^2 + x^4 ExpandAll[x^4*f[1/x]] a=Table[ SeriesCoefficient[ Series[x/(1-22 x^2-54 x^3-38 x^4),{x,0,50}],n],{n,0,50}]

%t CoefficientList[Series[x/(1-22 x^2-54 x^3-38 x^4),{x,0,30}],x] (* or *) LinearRecurrence[{0,22,54,38},{0,1,0,22},31] (* _Harvey P. Dale_, Aug 12 2011 *)

%K nonn

%O 1,4

%A _Roger L. Bagula_, Sep 15 2006

%E Edited by _N. J. A. Sloane_, Serp 17 2006