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Expansion of 1/((1-x)(1-4x)(1-5x)(1-8x)).
1

%I #17 May 17 2023 12:11:26

%S 1,18,215,2160,19821,172638,1456915,12056220,98541641,799142058,

%T 6448579215,51871439880,416407919461,3338534836278,26744994007115,

%U 214144960297140,1714090450201281,13717400347223298,109762678131820615

%N Expansion of 1/((1-x)(1-4x)(1-5x)(1-8x)).

%H Vincenzo Librandi, <a href="/A021764/b021764.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (18,-109,252,-160).

%F G.f.: 1/((1-x)*(1-4*x)*(1-5*x)*(1-8*x)).

%F a(n) = -1/84 +4^(n+2)/3 -5^(n+3)/12 +2^(3n+7)/21. - _Bruno Berselli_, May 07 2013

%F a(n) = 18*a(n-1) - 109*a(n-2) + 252*a(n-3) - 160*a(n-4). - _Wesley Ivan Hurt_, May 17 2023

%t CoefficientList[Series[1/((1 - x) (1 - 4 x) (1 - 5 x) (1 - 8 x)), {x, 0, 20}], x] (* _Bruno Berselli_, May 07 2013 *)

%t LinearRecurrence[{18,-109,252,-160},{1,18,215,2160},30] (* _Harvey P. Dale_, Jul 28 2015 *)

%o (PARI) Vec(1/((1-x)*(1-4*x)*(1-5*x)*(1-8*x))+O(x^20)) \\ _Bruno Berselli_, May 07 2013

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-4*x)*(1-5*x)*(1-8*x)))); // _Bruno Berselli_, May 07 2013

%Y Cf. A018250 (first differences).

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.