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A021268 Expansion of 1/((1-x)(1-2x)(1-8x)(1-10x)). 1

%I

%S 1,21,305,3825,44481,494721,5346625,56661825,592183361,6126355521,

%T 62899732545,642086748225,6525582872641,66093551865921,

%U 667637303808065,6729987319337025,67728787443552321,680719188437241921

%N Expansion of 1/((1-x)(1-2x)(1-8x)(1-10x)).

%H Vincenzo Librandi, <a href="/A021268/b021268.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (21,-136,276,-160).

%F a(n) = (7*10^(n+3) - 12*8^(n+3) + 21*2^(n+3) - 16)/1008. [_Yahia Kahloune_, Jun 30 2013]

%F a(0)=1, a(1)=21, a(2)=305, a(3)=3825; for n>3, a(n) = 21*a(n-1) -136*a(n-2) +276*a(n-3) -160*a(n-4). - _Vincenzo Librandi_, Jul 08 2013

%F a(0)=1, a(1)=21; for n>1, a(n) = 18*a(n-1) -80*a(n-2) +2^n -1. - _Vincenzo Librandi_, Jul 08 2013

%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 8 x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 08 2013 *)

%o (MAGMA) I:=[1, 21, 305, 3825]; [n le 4 select I[n] else 21*Self(n-1)-136*Self(n-2)+276*Self(n-3)-160*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-8*x)*(1-10*x)))); // _Vincenzo Librandi_, Jul 08 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.

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Last modified August 12 23:19 EDT 2020. Contains 336440 sequences. (Running on oeis4.)