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A021594 Expansion of 1/((1-x)(1-3x)(1-7x)(1-9x)). 1

%I #16 Sep 08 2022 08:44:45

%S 1,20,270,3100,32711,328440,3195340,30437000,285695421,2653625260,

%T 24459281210,224170373700,2045792060131,18609941810480,

%U 168874176353880,1529560509125200,13833895100278841,124980009723284100

%N Expansion of 1/((1-x)(1-3x)(1-7x)(1-9x)).

%H Vincenzo Librandi, <a href="/A021594/b021594.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,-130,300,-189).

%F a(n) = (9^(n+3)-2*7^(n+3)+2*3^(n+3)-1)/96. - _Yahia Kahloune_, May 23 2013

%F a(0)=1, a(1)=20; for n>1, a(n) = 16*a(n-1) -63*a(n-2) +(3^n - 1)/2. - _Vincenzo Librandi_, Jul 11 2013

%F a(0)=1, a(1)=20, a(2)=270, a(3)=3100; for n>3, a(n) = 20*a(n-1) -130*a(n-2) +300*a(n-3) -189*a(n-4). - _Vincenzo Librandi_, Jul 11 2013

%t CoefficientList[Series[1 / ((1 -x) (1 - 3 x) (1 - 7 x) (1 - 9 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 11 2013 *)

%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-7*x)*(1-9*x)))); /* or */ I:=[1, 20, 270, 3100]; [n le 4 select I[n] else 20*Self(n-1)-130*Self(n-2)+300*Self(n-3)-189*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 11 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)