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Expansion of (1-2*x)/((1-x)^3*(1-4*x)).
1

%I #9 Apr 16 2016 03:17:24

%S 1,5,20,78,307,1219,4862,19428,77685,310705,1242776,4971050,19884135,

%T 79536463,318145762,1272582944,5090331657,20361326493,81445305820,

%U 325781223110,1303124892251,5212499568795,20849998274950,83399993099548,333599972397917

%N Expansion of (1-2*x)/((1-x)^3*(1-4*x)).

%H Colin Barker, <a href="/A028814/b028814.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 (7,-15,13,-4).

%F From _Colin Barker_, Apr 16 2016: (Start)

%F a(n) = (-10+4^(3+n)+15*n+9*n^2)/54.

%F a(n) = 6*a(n-1)-8*a(n-2)-2*a(n-3)+9*a(n-4)-4*a(n-5) for n>3.

%F (End)

%t LinearRecurrence[{7, -15, 13, -4}, {1, 5, 20, 78}, 25] (* _Vaclav Kotesovec_, Apr 16 2016 *)

%o (PARI) Vec((1-2*x)/((1-x)^3*(1-4*x)) + O(x^50)) \\ _Colin Barker_, Apr 16 2016

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_