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%I #16 Sep 08 2022 08:44:48
%S 1,27,488,7434,103215,1353681,17093182,210149568,2533379189,
%T 30086951895,353166486036,4106992533462,47398834914523,
%U 543607880403069,6201901277261450,70443098125125516,797096110863739617
%N Expansion of 1/((1-x)(1-5x)(1-10x)(1-11x)).
%H Vincenzo Librandi, <a href="/A023946/b023946.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 (27,-241,765,-550).
%F a(n) = (6*11^(n+3) - 8*10^(n+3) + 3*5^(n+3) -1)/360. [_Yahia Kahloune_, Jun 27 2013]
%F a(0)=1, a(1)=27, a(2)=488, a(3)=7434; for n>3, a(n) = 27*a(n-1) -241*a(n-2) +765*a(n-3) -550*a(n-4). - _Vincenzo Librandi_, Jul 12 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 5 x) (1 - 10 x) (1 - 11 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 12 2013 *)
%t LinearRecurrence[{27,-241,765,-550},{1,27,488,7434},20] (* _Harvey P. Dale_, Jan 14 2015 *)
%o (Magma) I:=[1,27,488,7434]; [n le 4 select I[n] else 27*Self(n-1)-241*Self(n-2)+765*Self(n-3)-550*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-10*x)*(1-11*x)))); // _Vincenzo Librandi_, Jul 12 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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