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%I #20 Sep 08 2022 08:44:41
%S 1,24,412,6192,86800,1166592,15249088,195489024,2470868224,
%T 30900418560,383305022464,4724660269056,57945923227648,
%U 707851078729728,8619212944752640,104680555337023488,1268666664044265472
%N Expansion of 1/((1-2x)(1-10x)(1-12x)).
%H Vincenzo Librandi, <a href="/A016326/b016326.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 (24,-164, 240).
%F From _Vincenzo Librandi_, Oct 09 2011: (Start)
%F a(n) = (12^(n+2)+2^n-125*10^n)/20.
%F a(n) = 22*a(n-1) - 120*a(n-2) + 2^n.
%F a(n) = 24*a(n-1) - 164*a(n-2) + 240*a(n-3), n>=3. (End)
%t CoefficientList[Series[1/((1-2x)(1-10x)(1-12x)),{x,0,20}],x] (* or *) LinearRecurrence[{24,-164,240},{1,24,412},20] (* _Harvey P. Dale_, Aug 30 2014 *)
%o (Magma) [(12^(n+2)+2^n-125*10^n)/20 : n in [0..20]]; // _Vincenzo Librandi_, Oct 09 2011
%o (PARI) Vec(1/((1-2*x)*(1-10*x)*(1-12*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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