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Expansion of 1/((1-2x)(1-3x)(1-4x)(1-10x)).
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%I #16 Jun 13 2015 00:49:05

%S 1,19,245,2735,28701,293079,2957125,29682895,297294701,2974868039,

%T 29756539605,297597360255,2976103045501,29761552993399,

%U 297617634403685,2976184804896815,29761882021417101,297618956491125159

%N Expansion of 1/((1-2x)(1-3x)(1-4x)(1-10x)).

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (19,-116,284,-240).

%F a(n) = 19*a(n-1) - 116*a(n-2) + 284*a(n-3) - 240*a(n-4), with a(0)=1, a(1)=19, a(2)=245, a(3)=2735. [_Harvey P. Dale_, Oct 18 2011]

%F a(n) = (10^(n+3) - 7*4^(n+4) + 16*3^(n+4) - 21*2^(n+3))/336. - _Yahia Kahloune_, May 19 2013

%t CoefficientList[Series[1/((1-2x)(1-3x)(1-4x)(1-10x)),{x,0,30}],x] (* or *) LinearRecurrence[{19,-116,284,-240},{1,19,245,2735},31] (* _Harvey P. Dale_, Oct 18 2011 *)

%o (PARI) Vec((-4560*x^3 + 5156*x^2 - 1920*x + 245)/(240*x^4 - 284*x^3 + 116*x^2 - 19*x + 1)+O(x^99)) \\ _Charles R Greathouse IV_, May 20 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.