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%I #16 Aug 12 2023 16:41:59
%S 1,20,277,3324,37149,398916,4181269,43157708,440992717,4475837652,
%T 45219751941,455427151452,4576878947005,45927041513828,
%U 460378179477493,4611536145214956,46169641905360813,462076382226349044
%N Expansion of 1/((1-x)(1-2x)(1-7x)(1-10x)).
%H Vincenzo Librandi, <a href="/A021234/b021234.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 (20,-123,244,-140).
%F a(n) = (5*10^(n+3) - 12*7^(n+3) + 27*2^(n+3) - 20)/1080. [_Yahia Kahloune_, Jul 07 2013]
%F a(0)=1, a(1)=20, a(2)=277, a(3)=3324; for n>3, a(n) = 20*a(n-1) -123*a(n-2) +244*a(n-3) -140*a(n-4). - _Vincenzo Librandi_, Jul 08 2013
%F a(0)=1, a(1)=20; for n>1, a(n) = 17*a(n-1) -70*a(n-2) +2^n -1. - _Vincenzo Librandi_, Jul 08 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 7 x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 08 2013 *)
%t LinearRecurrence[{20,-123,244,-140},{1,20,277,3324},20] (* _Harvey P. Dale_, Aug 12 2023 *)
%o (Magma) I:=[1, 20, 277, 3324]; [n le 4 select I[n] else 20*Self(n-1)-123*Self(n-2)+244*Self(n-3)-140*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-7*x)*(1-10*x)))); // _Vincenzo Librandi_, Jul 08 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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