%I #32 Oct 02 2023 11:43:00
%S 1,9,54,264,1134,4446,16272,56412,187137,598417,1854882,5597172,
%T 16498632,47638512,135048672,376592064,1034663040,2804590080,
%U 7509232640,19880294400,52088352768,135173578752,347680161792,886900948992,2245014454272,5641949085696
%N Expansion of ((1-x)/(1-2x))^9.
%C a(n) is the number of weak compositions of n with exactly 8 parts equal to 0. - _Milan Janjic_, Jun 27 2010
%H Vincenzo Librandi, <a href="/A169796/b169796.txt">Table of n, a(n) for n = 0..1000</a>
%H Nickolas Hein, Jia Huang, <a href="https://arxiv.org/abs/1807.04623">Variations of the Catalan numbers from some nonassociative binary operations</a>, arXiv:1807.04623 [math.CO], 2018.
%H M. Janjic and B. Petkovic, <a href="http://arxiv.org/abs/1301.4550">A Counting Function</a>, arXiv 1301.4550 [math.CO], 2013.
%H M. Janjic, B. Petkovic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Janjic/janjic45.html">A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers</a>, J. Int. Seq. 17 (2014) # 14.3.5.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (18, -144, 672, -2016, 4032, -5376, 4608, -2304, 512).
%F G.f.: ((1-x)/(1-2*x))^9.
%F For n > 0, a(n) = 2^(n-16)*(n+8)*(n^7 + 100*n^6 + 3778*n^5 + 68056*n^4 + 606961*n^3 + 2543284*n^2 + 4524300*n + 2575440)/315. - _Bruno Berselli_, Aug 07 2011
%t CoefficientList[Series[((1 - x)/(1 - 2 x))^9, {x, 0, 25}], x] (* _Michael De Vlieger_, Oct 15 2018 *)
%Y Cf. for ((1-x)/(1-2x))^k: A011782, A045623, A058396, A062109, A169792-A169797; a row of A160232.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, May 15 2010