A023948 - OEIS

%I #18 Jun 30 2026 19:44:02

%S 1,29,566,9346,141027,2013855,27722632,371889332,4894555493,

%T 63487825921,814150878138,10345138210758,130470568108999,

%U 1635266348565827,20389018656020684,253092309224759224

%N Expansion of 1/((1-x)(1-5x)(1-11x)(1-12x)).

%H Vincenzo Librandi, <a href="/A023948/b023948.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 (29,-275,907,-660).

%F a(0)=1, a(1)=29, a(2)=566, a(3)=9346; for n>3, a(n) = 29*a(n-1)- 275*a(n-2)+ 907*a(n-3)- 660*a(n-4). [_Harvey P. Dale_, Jun 20 2011]

%F a(n) = (5*2^(2*n+7)*3^(n+3)+11*5^(n+3)-14*11^(n+3)-21)/9240. [_Harvey P. Dale_, Jun 20 2011]

%t CoefficientList[Series[1/((1-x)(1-5x)(1-11x)(1-12x)),{x,0,30}],x] (* _Harvey P. Dale_, Jun 20 2011 *)

%t (* Alternative: *)

%t LinearRecurrence[{29,-275,907,-660},{1,29,566,9346},30] (* _Harvey P. Dale_, Jun 20 2011 *)

%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-11*x)*(1-12*x)))); // _Vincenzo Librandi_, Jul 12 2013

%K nonn,easy,changed

%O 0,2

%A _N. J. A. Sloane_