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A021974 Expansion of 1/((1-x)(1-4x)(1-9x)(1-12x)). 1

%I

%S 1,26,459,6916,96005,1270542,16318303,205487672,2552951769,

%T 31419668098,384095637107,4672689817068,56644179720493,

%U 684877363365494,8264853578776071,99595171342479904,1198894417410885377

%N Expansion of 1/((1-x)(1-4x)(1-9x)(1-12x)).

%H Vincenzo Librandi, <a href="/A021974/b021974.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 (26,-217,624,-432).

%F a(n) = (5*12^(n+3) - 11*9^(n+3) + 11*4^(n+3) - 5)/1320. [_Yahia Kahloune_, Jul 05 2013]

%F a(0)=1, a(1)=26, a(2)=459, a(3)=6916; for n>3, a(n) = 26*a(n-1) -217*a(n-2) +624*a(n-3) -432*a(n-4). - _Vincenzo Librandi_, Jul 11 2013

%t CoefficientList[Series[1 / ((1 - x) (1 - 4 x) (1 - 9 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 11 2013 *)

%o (MAGMA) I:=[1,26,459,6916]; [n le 4 select I[n] else 26*Self(n-1)-217*Self(n-2)+624*Self(n-3)-432*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-4*x)*(1-9*x)*(1-12*x)))); // _Vincenzo Librandi_, Jul 11 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.

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Last modified May 27 16:48 EDT 2022. Contains 354110 sequences. (Running on oeis4.)