login
Expansion of 1/((1-x)*(1-5*x)*(1-8*x)*(1-11*x)).
1

%I #24 Sep 08 2022 08:44:46

%S 1,25,418,5898,76059,930003,10996396,127188916,1449394837,16348318701,

%T 183083516694,2039995806654,22648876033135,250810539522919,

%U 2772306789414112,30602539667823912,337485446955075753,3719200955052251457,40966103582317693450,451066307861295957490

%N Expansion of 1/((1-x)*(1-5*x)*(1-8*x)*(1-11*x)).

%H Vincenzo Librandi, <a href="/A022628/b022628.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (25,-207,623,-440).

%F a(n) = (14*11^(n+3) - 40*8^(n+3) + 35*5^(n+3) - 9)/2520. - _Yahia Kahloune_, Jun 29 2013

%F a(0)=1, a(1)=25, a(2)=418, a(3)=5898; for n > 3, a(n) = 25*a(n-1) - 207*a(n-2) + 623*a(n-3) - 440*a(n-4). - _Vincenzo Librandi_, Jul 12 2013

%p [seq(coeftayl(1/((1-x)*(1-5*x)*(1-8*x)*(1-11*x)), x = 0, k), k=1..20)]; # _Muniru A Asiru_, Feb 17 2018

%t CoefficientList[Series[1/((1-x)*(1-5*x)*(1-8*x)*(1-11*x)), {x,0,20}], x] (* _Vincenzo Librandi_, Jul 12 2013 *)

%t Table[(14*11^(n+3) -40*8^(n+3) +35*5^(n+3) -9)/2520, {n,0,30}] (* _G. C. Greubel_, feb 16 2018 *)

%t LinearRecurrence[{25,-207,623,-440},{1,25,418,5898},20] (* _Harvey P. Dale_, May 23 2021 *)

%o (Magma) I:=[1, 25, 418, 5898]; [n le 4 select I[n] else 25*Self(n-1)-207*Self(n-2)+623*Self(n-3)-440*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-8*x)*(1-11*x)))); // _Vincenzo Librandi_, Jul 12 2013

%o (PARI) x='x+O('x^30); Vec(1/((1-x)*(1-5*x)*(1-8*x)*(1-11*x))) \\ _G. C. Greubel_, Feb 16 2018

%o (GAP) A022628:=List([0..20],n->(14*11^(n+3)-40*8^(n+3)+35*5^(n+3)-9)/2520); # _Muniru A Asiru_, Feb 17 2018

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_