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%I #23 Sep 08 2022 08:44:40
%S 1,15,169,1755,17761,178275,1784809,17854395,178563121,1785689235,
%T 17857067449,178571201835,1785713604481,17857140811395,
%U 178571422430089,1785714267282075,17857142801829841,178571428405456755
%N Expansion of 1/((1-2x)(1-3x)(1-10x)).
%H Vincenzo Librandi, <a href="/A016279/b016279.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 (15,-56,60).
%F a(n) = 2^n/2 - 9*3^n/7 + 25*10^n/14. - _Antonio Alberto Olivares_, Feb 03 2010
%F a(n) = 15*a(n-1) - 56*a(n-2) + 60*a(n-3). - _Vincenzo Librandi_, Jun 24 2013
%t CoefficientList[Series[1 / ((1 - 2 x) (1 - 3 x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jun 24 2013 *)
%t LinearRecurrence[{15,-56,60},{1,15,169},30] (* _Harvey P. Dale_, Jul 07 2013 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-2*x)*(1-3*x)*(1-10*x)))); /* or */ I:=[1, 15, 169]; [n le 3 select I[n] else 15*Self(n-1)-56*Self(n-2)+60*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jun 24 2013
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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