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Expansion of 1/((1-x)(1-4x)(1-5x)(1-10x)).
1

%I #12 Sep 08 2022 08:44:45

%S 1,20,271,3150,34041,354480,3620611,36607010,368161981,3692428740,

%T 36979730151,370080107670,3702237477121,37029646251800,

%U 370333177834891,3703516786589130,37036098633715461,370365663082767660

%N Expansion of 1/((1-x)(1-4x)(1-5x)(1-10x)).

%H Vincenzo Librandi, <a href="/A021774/b021774.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 (20,-129,310,-200).

%F G.f.: 1/((1-x)*(1-4*x)*(1-5*x)*(1-10*x)).

%F a(n) = -1/108 +2^(2n+5)/9 -5^(n+2)/4 +10^(n+2)/27. [_Bruno Berselli_, May 08 2013]

%t CoefficientList[Series[1/((1 - x) (1 - 4 x) (1 - 5 x) (1 - 10 x)), {x, 0, 20}], x] (* _Bruno Berselli_, May 08 2013 *)

%o (PARI) Vec(1/((1-x)*(1-4*x)*(1-5*x)*(1-10*x))+O(x^20)) \\ _Bruno Berselli_, May 08 2013

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-4*x)*(1-5*x)*(1-10*x)))); // _Bruno Berselli_, May 08 2013

%Y Cf. A018912 (first differences).

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.