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A019928 Expansion of 1/((1-5x)(1-7x)(1-8x)). 2

%I

%S 1,20,269,3040,31161,300300,2775109,24887960,218303921,1882786180,

%T 16026538749,135010883280,1127921219881,9359429537660,77233958267189,

%U 634411837477000,5191228487083041,42342127346986740

%N Expansion of 1/((1-5x)(1-7x)(1-8x)).

%H Vincenzo Librandi, <a href="/A019928/b019928.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,-131,280).

%F a(n) = 25*5^n/6 -49*7^n/2 +64*8^n/3. - _R. J. Mathar_, Jun 29 2013

%F a(0)=1, a(1)=20, a(2)=269; for n>2, a(n) = 20*a(n-1) -131*a(n-2) +280*a(n-3). - _Vincenzo Librandi_, Jul 03 2013

%F a(n) = 15*a(n-1) -56*a(n-2) +5^n. - _Vincenzo Librandi_, Jul 03 2013

%t CoefficientList[Series[1 / ((1 - 5 x) (1 - 7 x) (1 - 8 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 03 2013 *)

%o (MAGMA) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-7*x)*(1-8*x)))); /* or */ I:=[1, 20, 269]; [n le 3 select I[n] else 20*Self(n-1)-131*Self(n-2)+280*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 03 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.

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Last modified April 23 02:15 EDT 2019. Contains 322380 sequences. (Running on oeis4.)