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%I #17 Sep 08 2022 08:44:45
%S 1,16,179,1766,16545,151572,1374943,12417922,111935549,1008117968,
%T 9075855867,81693883518,735289682713,6617786085004,59560790560151,
%U 536049978287354,4824461257701237,43420197132033480
%N Expansion of 1/((1-x)(1-2x)(1-4x)(1-9x)).
%H Vincenzo Librandi, <a href="/A021084/b021084.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 (16,-77,134,-72).
%F a(0)=1, a(1)=16; for n>1, a(n) = 13*a(n-1) -36*a(n-2)+ 2^n - 1. - _Vincenzo Librandi_, Jul 06 2013
%F a(0)=1, a(1)=16, a(2)=179, a(3)=1766; for n>3, a(n) = 16*a(n-1) -77*a(n-2) +134*a(n-3) -72*a(n-4). - _Vincenzo Librandi_, Jul 06 2013
%F a(n) = (3*9^(n+3) - 28*4^(n+3) + 60*2^(n+3) - 35)/840. [_Yahia Kahloune_, Jul 07 2013]
%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 4 x) (1 - 9 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 06 2013 *)
%o (PARI) Vec(1/((1-x)*(1-2*x)*(1-4*x)*(1-9*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-4*x)*(1-9*x)))); /* or */ I:=[1, 16, 179, 1766]; [n le 4 select I[n] else 16*Self(n-1)-77*Self(n-2)+134*Self(n-3)-72*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 06 2013
%Y Cf. A016291.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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