%I #25 Sep 08 2022 08:44:41
%S 1,21,313,4065,49081,566721,6350473,69654225,751887961,8016991521,
%T 84652923433,886876310385,9231886792441,95586981129921,
%U 985282830165193,10117545471478545,103557909243290521,1057021183189581921
%N Expansion of 1/((1-2x)(1-9x)(1-10x)).
%H Vincenzo Librandi, <a href="/A016321/b016321.txt">Table of n, a(n) for n = 0..900</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (21,-128,180).
%F From _Zerinvary Lajos_, Jun 05 2009 [corrected by _R. J. Mathar_, Mar 14 2011]: (Start)
%F a(n) = 2^(n-1)/7 - 9^(n+2)/7 + 25*10^n/2.
%F a(n) = A016134(n+1) - A016133(n+1). (End)
%F From _Vincenzo Librandi_, Oct 09 2011: (Start)
%F a(n) = (175*10^n + 2^n - 2*9^(n+2))/14.
%F a(n) = 19*a(n-1) - 90*a(n-2) + 2^n.
%F a(n) = 21*a(n-1) - 128*a(n-2) + 180*a(n-3), n >= 3. (End)
%t CoefficientList[Series[1/((1-2x)(1-9x)(1-10x)),{x,0,20}],x] (* or *) LinearRecurrence[{21,-128,180},{1,21,313},20] (* _Harvey P. Dale_, Aug 18 2014 *)
%o (Sage) [(10^n - 2^n)/8-(9^n - 2^n)/7 for n in range(2,20)] # _Zerinvary Lajos_, Jun 05 2009
%o (Magma) [(175*10^n +2^n-2*9^(n+2))/14 : n in [0..20]]; // _Vincenzo Librandi_, Oct 09 2011
%o (PARI) a(n) = (175*10^n+2^n-162*9^n)/14 \\ _Charles R Greathouse IV_, Sep 23 2012
%Y Cf. A016133, A016134.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_