%I #14 Sep 08 2022 08:44:45

%S 1,21,304,3822,45031,513639,5760910,64038576,708445573,7817058249,

%T 86132670988,948329828082,10436851589347,114836710756971,

%U 1263391885146058,13898439159046260,152889601348716673

%N Expansion of 1/((1-x)(1-3x)(1-6x)(1-11x)).

%H Vincenzo Librandi, <a href="/A021524/b021524.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,-137,315,-198).

%F a(n) = (3*11^(n+3) - 16*6^(n+3) + 25*3^(n+3) - 12)/1200. [_Yahia Kahloune_, Jun 30 2013]

%F a(0)=1, a(1)=21; for n>1, a(n) = 17*a(n-1) -66*a(n-2) +(3^n - 1)/2. - _Vincenzo Librandi_, Jul 10 2013

%F a(0)=1, a(1)=21, a(2)=304, a(3)=3822; for n>3, a(n) = 21*a(n-1) -137*a(n-2) +315*a(n-3)- 198*af(n-4). - _Vincenzo Librandi_, Jul 10 2013

%t CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 6 x) (1 - 11 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 10 2013 *)

%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-6*x)*(1-11*x)))); /* or */ I:=[1, 21, 304, 3822]; [n le 4 select I[n] else 21*Self(n-1)-137*Self(n-2)+315*Self(n-3)-198*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 10 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.