%I #27 Sep 08 2022 08:44:41
%S 1,20,284,3520,40656,450240,4851904,51315200,535521536,5534172160,
%T 56773377024,579187015680,5883496124416,59567968993280,
%U 601543751942144,6062350015528960,60998800124215296,612990400993689600
%N Expansion of 1/((1-2x)(1-8x)(1-10x)).
%H Vincenzo Librandi, <a href="/A016317/b016317.txt">Table of n, a(n) for n = 0..900</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (20,-116, 160).
%F From _Vincenzo Librandi_, Oct 09 2011: (Start)
%F a(n) = (75*10^n + 2^n - 8^(n+2))/12.
%F a(n) = 18*a(n-1) - 80*a(n-2) + 2^n.
%F a(n) = 20*a(n-1) - 116*a(n-2) + 160*a(n-3), n >= 3. (End)
%t CoefficientList[Series[1/((1 - 2 x) (1 - 8 x) (1 - 10 x)), {x, 0, 17}], x] (* _Michael De Vlieger_, Jan 31 2018 *)
%t LinearRecurrence[{20,-116,160},{1,20,284},20] (* _Harvey P. Dale_, Mar 20 2020 *)
%o (Sage) [((10^n - 2^n)/8-(8^n - 2^n)/6)/2 for n in range(2,20)] # _Zerinvary Lajos_, Jun 05 2009
%o (Magma) [((75*10^n + 2^n -8^(n+2))/12) : n in [0..20]]; // _Vincenzo Librandi_, Oct 09 2011
%o (PARI) Vec(1/((1-2*x)*(1-8*x)*(1-10*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_