%I #16 Sep 08 2022 08:44:48
%S 1,25,416,5822,74319,898779,10511446,120335968,1358681621,15202492877,
%T 169098946380,1873624439778,20707233183547,228476788273759,
%U 2518219270791458,27735798399148292,305344872665615937
%N Expansion of 1/((1-x)(1-6x)(1-7x)(1-11x)).
%H Vincenzo Librandi, <a href="/A023952/b023952.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 (25,-209,647,-462).
%F a(0)=1, a(1)=25, a(2)=416, a(3)=5822, a(n)=25*a(n-1)-209*a(n-2)+ 647*a(n-3)- 462*a(n-4) [_Harvey P. Dale_, Mar 24 2012]
%F a(n) = (3*11^(n+3) - 25*7^(n+3) + 24*6^(n+3) - 2)/600. [_Yahia Kahloune_, Jun 29 2013]
%t CoefficientList[Series[1 / ((1 - x) (1 - 6 x) (1 - 7 x) (1 - 11 x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{25, -209, 647, -462}, {1, 25, 416, 5822}, 30] (* _Harvey P. Dale_, Mar 24 2012 *)
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-6*x)*(1-7*x)*(1-11*x)))); /* or */ I:=[1, 25, 416, 5822]; [n le 4 select I[n] else 25*Self(n-1)-209*Self(n-2)+647*Self(n-3)-462*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 13 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.