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%I #16 Sep 08 2022 08:44:45
%S 1,20,287,3694,45609,553776,6677779,80295938,964364717,11576444932,
%T 138937682871,1667353916982,20008755624625,240107610616088,
%U 2881304043028763,34575712094589226,414908863026422133
%N Expansion of 1/((1-x)*(1-2*x)*(1-5*x)*(1-12*x)).
%H Vincenzo Librandi, <a href="/A021164/b021164.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,-113,214,-120).
%F a(0)=1, a(1)=20; for n>1, a(n) = 17*a(n-1) -60*a(n-2) +2^n -1. - _Vincenzo Librandi_, Jul 07 2013
%F a(0)=1, a(1)=20, a(2)=287, a(3)=3694; for n>3, a(n) = 20*a(n-1) -113*a(n-2) +214*a(n-3)-120*a(n-4). - _Vincenzo Librandi_, Jul 07 2013
%F a(n) = (6*12^(n+3) - 11*5^(n+4) + 77*2^(n+4) - 105)/4620. [_Yahia Kahloune_, Jul 07 2013]
%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 5 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 07 2013 *)
%t LinearRecurrence[{20,-113,214,-120},{1,20,287,3694},20] (* _Harvey P. Dale_, Nov 15 2013 *)
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-5*x)*(1-12*x)))); /* or */ I:=[1, 20, 287, 3694]; [n le 4 select I[n] else 20*Self(n-1)-113*Self(n-2)+214*Self(n-3)-120*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 07 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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