%I #19 Sep 08 2022 08:44:50

%S 1,21,286,3234,33187,322455,3035152,28040628,256229413,2326373049,

%T 21042916258,189930286182,1712158289479,15423616827003,

%U 138884571944404,1250325501927096,11254768340210185,101302177508279517

%N Expansion of 1/((1-3*x)*(1-4*x)*(1-5*x)*(1-9*x)).

%H Vincenzo Librandi, <a href="/A028028/b028028.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (21, -155, 483, -540).

%F a(n) = (243/40)*9^n - (125/8)*5^n + (64/5)*4^n - (9/4)*3^n. - Neven Juric, Oct 22 2009

%F a(n) = 21*a(n-1) - 155*a(n-2) + 483*a(n-3) - 540*a(n-4); a(0)=1, a(1)=21, a(2)=286, a(3)=3234. - _Harvey P. Dale_, Aug 11 2011

%t CoefficientList[Series[1/((1-3x)(1-4x)(1-5x)(1-9x)),{x,0,30}],x] (* or *) LinearRecurrence[{21,-155,483,-540},{1,21,286,3234},30] (* _Harvey P. Dale_, Aug 11 2011 *)

%o (Magma) [(243/40)*9^n - (125/8)*5^n + (64/5)*4^n - (9/4)*3^n: n in [0..20]]; // _Vincenzo Librandi_, Aug 12 2011

%o (PARI) Vec(1/((1-3*x)*(1-4*x)*(1-5*x)*(1-9*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 27 2012

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_