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%I #19 Sep 08 2022 08:44:45
%S 1,17,192,1822,15743,128499,1010374,7741184,58209525,431623621,
%T 3166395596,23035216386,166469995147,1196633240183,8564499500658,
%U 61079918944228,434330031817409,3080934011678985,21810281396626360
%N Expansion of 1/((1-x)(1-3x)(1-6x)(1-7x)).
%H Vincenzo Librandi, <a href="/A021494/b021494.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 (17,-97,207,-126).
%F a(n) = (5*7^(n+3) - 8*6^(n+3) + 5*3^(n+3) - 2)/120. [_Yahia Kahloune_, Jul 05 2013]
%F a(0)=1, a(1)=17; for n>1, a(n) = 13*a(n-1) -42*a(n-2) +(3^n -1)/2. - _Vincenzo Librandi_, Jul 10 2013
%F a(0)=1, a(1)=17, a(2)=192, a(3)=1822; for n>3, a(n) = 17*a(n-1) -97*a(n-2) +207*a(n-3) -126*a(n-4). - _Vincenzo Librandi_, Jul 10 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 6 x) (1 - 7 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 10 2013 *)
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-6*x)*(1-7*x)))); /* or */ I:=[1, 17, 192, 1822]; [n le 4 select I[n] else 17*Self(n-1)-97*Self(n-2)+207*Self(n-3)-126*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 10 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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