%I #23 Sep 04 2017 03:51:13

%S 1,20,291,3730,44681,513240,5730271,62683550,675263061,7188478660,

%T 75807419051,793377882570,8251512054241,85374719599280,

%U 879483587504631,9026463398652790,92349281698986221,942254646401987100,9591402928728995011,97433737469672066210

%N Expansion of 1/((1-x)*(1-9*x)*(1-10*x)).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (20,-109,90).

%F a(n) = (8*10^(n+2) - 9^(n+3) + 1)/72. - _Bruno Berselli_, Mar 21 2011

%F a(n) = 19*a(n-1) - 90*a(n-2) + 1, n >= 2. - _Vincenzo Librandi_, Mar 21 2011

%t Table[(2^(n + 4)*5^(n + 1) - 9^(n + 2) + 1)/72, {n, 40}] (* or *) CoefficientList[Series[1/((1 - z) (1 - 9*z) (1 - 10*z)), {z, 0, 40}], z] (* _Vladimir Joseph Stephan Orlovsky_, Jul 21 2011 *)

%Y Cf. A016218, A016228.

%K nonn

%O 0,2

%A _N. J. A. Sloane_