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Expansion of 1/((1-x)(1-2x)(1-6x)(1-10x)).
1

%I #22 Sep 08 2022 08:44:45

%S 1,19,251,2891,31227,326235,3346267,33966427,342687323,3445012571,

%T 34558963803,346242670683,3466344910939,34686958350427,

%U 347010638983259,3470952722772059,34714605225488475,347176520241754203,3471948010339283035,34720576950924324955

%N Expansion of 1/((1-x)(1-2x)(1-6x)(1-10x)).

%H Vincenzo Librandi, <a href="/A021202/b021202.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,-110,212,-120).

%F a(n) = ( 5*10^(n+3)-18*6^(n+3)+45*2^(n+3)-32 )/1440. - _Yahia Kahloune_, May 20 2013

%F a(0)=1, a(1)=19; for n>1, a(n) = 16*a(n-1) -60*a(n-2) +2^n -1. - _Vincenzo Librandi_, Jul 08 2013

%F a(0)=1, a(1)=19, a(2)=251, a(3)=2891; for n>3, a(n) = 19*a(n-1) -110*a(n-2) +212*a(n-3) -120*a(n-4). - _Vincenzo Librandi_, Jul 08 2013

%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 6 x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 08 2013 *)

%t LinearRecurrence[{19,-110,212,-120},{1,19,251,2891},30] (* _Harvey P. Dale_, Apr 26 2015 *)

%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-6*x)*(1-10*x)))); /* or */ I:=[1, 19, 251, 2891]; [n le 4 select I[n] else 19*Self(n-1)-110*Self(n-2)+212*Self(n-3)-120*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 08 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.