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Expansion of 1/((1-x)(1-2x)(1-6x)(1-11x)).
1

%I #24 Nov 16 2024 20:18:52

%S 1,20,281,3472,40509,459564,5139121,57034088,630398021,6952517572,

%T 76586531385,843104877888,9278071860877,102082299710684,

%U 1123046352296513,12354356208201112,135902996287980117,1494963427154650740,16444780506622899145,180893682420383385200

%N Expansion of 1/((1-x)(1-2x)(1-6x)(1-11x)).

%H Vincenzo Librandi, <a href="/A021204/b021204.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 (20,-119,232,-132).

%F a(n) = (2*11^(n+3)-9*6^(n+3)+25*2^(n+3)-18)/900. - _Yahia Kahloune_, May 21 2013

%F a(0)=1, a(1)=20; for n>1, a(n) = 17*a(n-1) -66*a(n-2) +2^n -1. - _Vincenzo Librandi_, Jul 08 2013

%F a(0)=1, a(1)=20, a(2)=281, a(3)=3472; for n>3, a(n) = 20*a(n-1) -119*a(n-2) +232*a(n-3) -132*a(n-4). - _Vincenzo Librandi_, Jul 08 2013

%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 6 x) (1 - 11 x)), {x, 0, 30}], x] (* _Harvey P. Dale_, Mar 12 2011 *)

%o (PARI) x='x+O('x^66); Vec(1/((1-x)*(1-2*x)*(1-6*x)*(1-11*x))) \\ _Joerg Arndt_, May 21 2013

%o (Magma) I:=[1, 20, 281, 3472]; [n le 4 select I[n] else 20*Self(n-1)-119*Self(n-2)+232*Self(n-3)-132*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 08 2013

%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-6*x)*(1-11*x)))); // _Vincenzo Librandi_, Jul 08 2013

%K nonn,easy,changed

%O 0,2

%A _N. J. A. Sloane_.