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Expansion of 1/((1-x)(1-4x)(1-10x)(1-20x)).
3

%I #22 Sep 08 2022 08:45:09

%S 1,35,871,19215,402591,8236095,166570111,3349906175,67183250431,

%T 1345516627455,26928850135551,538762184167935,10777095520297471,

%U 215560428864815615,4311393762242888191,86229727095755178495

%N Expansion of 1/((1-x)(1-4x)(1-10x)(1-20x)).

%C Column k=3 in number triangle A080249.

%H Vincenzo Librandi, <a href="/A080250/b080250.txt">Table of n, a(n) for n = 0..300</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (35,-354,1120,-800).

%F G.f.: 1/((1-x)*(1-4*x)*(1-10*x)*(1-20*x)).

%F a(n) = (1350*20^n-950*10^n+114*4^n-1)/513.

%F a(0)=1, a(1)=35, a(2)=871, a(3)=19215, a(n) = 35*a(n-1) -354*a(n-2) +1120*a(n-3) -800*a(n-4). - _Harvey P. Dale_, Apr 25 2011

%t CoefficientList[Series[1/((1-x)(1-4x)(1-10x)(1-20x)),{x,0,20}],x] (* or *) Table[(1350*20^n-950*10^n+114*4^n-1)/513,{n,0,20}] (* or *) LinearRecurrence[{35,-354,1120,-800},{1,35,871,19215},21] (* _Harvey P. Dale_, Apr 25 2011 *)

%o (Magma) [(1350*20^n-950*10^n+114*4^n-1)/513: n in [0..20]]; // _Vincenzo Librandi_, Aug 05 2013

%Y Cf. A080249, A016225, A000292.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Feb 17 2003

%E Corrected by _T. D. Noe_, Nov 08 2006