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%I #55 Feb 12 2024 07:20:17
%S 1,11,103,935,8431,75911,683263,6149495,55345711,498111911,4483008223,
%T 40347076055,363123688591,3268113205511,29413018865983,
%U 264717169826615,2382454528505071,21442090756676711,192978816810352543,1736809351293697175,15631284161644323151
%N Expansion of 1/((1-2*x)*(1-9*x)).
%H Vincenzo Librandi, <a href="/A016133/b016133.txt">Table of n, a(n) for n = 0..1000</a>
%H Kalika Prasad, Munesh Kumari, Rabiranjan Mohanta, and Hrishikesh Mahato, <a href="https://arxiv.org/abs/2307.08073">The sequence of higher order Mersenne numbers and associated binomial transforms</a>, arXiv:2307.08073 [math.NT], 2023.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-18).
%F a(n) = 11*a(n-1) - 18*a(n-2).
%F a(n) = a(n) = 9*a(n-1) + 2^n. - _Paul Curtz_, Feb 14 2008
%F E.g.f.: exp(2*x)*(9*exp(7*x) - 2)/7. - _Stefano Spezia_, Jul 30 2022
%t CoefficientList[Series[1/((1-2x)(1-9x)),{x,0,30}],x] (* or *) LinearRecurrence[ {11,-18},{1,11},30] (* _Harvey P. Dale_, Apr 19 2020 *)
%o (Sage) [lucas_number1(n,11,18) for n in range(1, 20)] # _Zerinvary Lajos_, Apr 27 2009
%o (Magma) [+9^(n+1)/7 -2^(n+1)/7 : n in [0..20]]; // _Vincenzo Librandi_, Aug 14 2011
%o (PARI) Vec(1/((1-2*x)*(1-9*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 23 2012
%Y Cf. A016131, A016136.
%Y Cf. A016204 (partial sums); A191465 (this sequence times 7).
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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