%I #21 Sep 08 2022 08:44:45

%S 1,18,220,2310,22561,212268,1957600,17857620,161924521,1463379918,

%T 13200803980,118959425130,1071396569881,9646380238968,86836484875360,

%U 781623699024840,7035090031526641,63318194178965418

%N Expansion of 1/((1-x)(1-3x)(1-5x)(1-9x)).

%H Vincenzo Librandi, <a href="/A021454/b021454.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 (18,-104,222,-135).

%F a(0)=1, a(1)=18, a(2)=220, a(3)=2310, a(n)=18*a(n-1)- 104*a(n-2)+ 222*a(n-3)- 135*a(n-4). - _Harvey P. Dale_, Nov 05 2011

%F a(n) = (3*9^(n+2) - 2*5^(n+3) + 8*3^(n+2) - 1)/64. - _Yahia Kahloune_, Jun 26 2013

%F a(0)=1, a(1)=18; for n>1, a(n) = 14*a(n-1) -45*a(n-2) +(3^n-1)/2. - _Vincenzo Librandi_, Jul 10 2013

%t CoefficientList[Series[1/((1-x)(1-3x)(1-5x)(1-9x)),{x,0,20}],x] (* or *) LinearRecurrence[{18,-104,222,-135},{1,18,220,2310},20] (* _Harvey P. Dale_, Nov 05 2011 *)

%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-5*x)*(1-9*x)))); // _Vincenzo Librandi_, Jul 10 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.