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Expansion of 1/((1-x)(1-2x)(1-7x)(1-9x)).
1

%I #16 Sep 08 2022 08:44:45

%S 1,19,248,2786,28983,288273,2786566,26424112,247232645,2291004287,

%T 21080414004,192953358078,1759187655187,15990940940461,

%U 145026232803362,1312990445670284,11871194464243809,107220713350935195

%N Expansion of 1/((1-x)(1-2x)(1-7x)(1-9x)).

%H Vincenzo Librandi, <a href="/A021229/b021229.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,-113,221,-126).

%F a(n) = (15*9^(n+3) - 28*7^(n+3) + 48*2^(n+3) - 35)/1680. - _Yahia Kahloune_, May 19 2013

%F a(0)=1, a(1)=19, a(2)=248, a(3)=2786; for n>3, a(n) = 19*a(n-1) -113*a(n-2) +221*a(n-3) -126*a(n-4). - _Vincenzo Librandi_, Jul 08 2013

%F a(0)=1, a(1)=19; for n>1, a(n) = 16*a(n-1) -63*a(n-2) +2^n -1. - _Vincenzo Librandi_, Jul 08 2013

%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 7 x) (1 - 9 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 08 2013 *)

%t LinearRecurrence[{19,-113,221,-126},{1,19,248,2786},20]

%o (Magma) I:=[1, 19, 248, 2786]; [n le 4 select I[n] else 19*Self(n-1)-113*Self(n-2)+221*Self(n-3)-126*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-7*x)*(1-9*x)))); // _Vincenzo Librandi_, Jul 08 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.