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%I #22 Sep 08 2022 08:44:40
%S 1,14,145,1370,12541,113534,1023865,9221090,83008981,747138854,
%T 6724424785,60520350410,544684739821,4902167424974,44119521140905,
%U 397075733249330,3573681728253061,32163135941435894,289468224634660225
%N Expansion of 1/((1-2x)(1-3x)(1-9x)).
%H Vincenzo Librandi, <a href="/A016278/b016278.txt">Table of n, a(n) for n = 0..200</a>
%H Jeremiah Bartz, Bruce Dearden, and Joel Iiams, <a href="https://ajc.maths.uq.edu.au/pdf/77/ajc_v77_p318.pdf">Counting families of generalized balancing numbers</a>, The Australasian Journal of Combinatorics (2020) Vol. 77, Part 3, 318-325.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (14,-51,54).
%F a(n) = 14*a(n-1) - 51*a(n-2) + 54*a(n-3); a(n) = (4/7)*2^(n-1) + (-3/2)*3^(n-1) + (27/14)*9^(n-1). - _Antonio Alberto Olivares_, Apr 21 2008, Apr 22 2008
%t CoefficientList[Series[1 / ((1 - 2 x) (1 - 3 x) (1 - 9 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jun 24 2013 *)
%o (PARI) Vec(1/((1-2*x)*(1-3*x)*(1-9*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-2*x)*(1-3*x)*(1-9*x)))); // _Vincenzo Librandi_, Jun 24 2013
%Y Cf. A053141, A053142.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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