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A021464 Expansion of 1/((1-x)(1-3x)(1-5x)(1-10x)). 1

%I

%S 1,19,248,2810,29871,307929,3126478,31504000,316245941,3168518639,

%T 31715571108,317307900390,3173840747611,31742218586149,

%U 317441248586138,3174507821007980,31745554950382881,317457933399054459

%N Expansion of 1/((1-x)(1-3x)(1-5x)(1-10x)).

%H Vincenzo Librandi, <a href="/A021464/b021464.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 (19,-113,245,-150).

%F a(n) = (8*10^(n+3) - 63*5^(n+3) + 90*3^(n+3) - 35)/2520. - _Yahia Kahloune_, May 19 2013

%F a(0)=1, a(1)=19; for n>1, a(n) = 15*a(n-1)-50*a(n-2) +(3^n-1)/2. - _Vincenzo Librandi_, Jul 10 2013

%F a(0)=1, a(1)=19, a(2)=248, a(3)=2810; for n>3, a(n) = 19*a(n-1) -113*a(n-2) +245*a(n-3) -150*a(n-4). - _Vincenzo Librandi_, Jul 10 2013

%t CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 5 x) (1 -10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 10 2013 *)

%t LinearRecurrence[{19,-113,245,-150},{1,19,248,2810},30] (* _Harvey P. Dale_, Aug 05 2019 *)

%o (MAGMA) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-5*x)*(1-10*x)))); /* or */ I:=[1, 19, 248, 2810]; [n le 4 select I[n] else 19*Self(n-1)-113*Self(n-2)+245*Self(n-3)-150*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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Last modified July 31 18:30 EDT 2021. Contains 346376 sequences. (Running on oeis4.)