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%I #33 Oct 02 2023 11:41:47
%S 1,8,44,200,806,2984,10364,34232,108545,332688,990736,2878144,8182432,
%T 22823680,62595328,169090048,450568960,1185832960,3085885440,
%U 7947714560,20275478528,51272351744,128605356032,320145981440,791358537728,1943278714880,4742573981696
%N Expansion of ((1-x)/(1-2x))^8.
%C a(n) is the number of weak compositions of n with exactly 7 parts equal to 0. - _Milan Janjic_, Jun 27 2010
%H Vincenzo Librandi, <a href="/A169795/b169795.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_08">Index entries for linear recurrences with constant coefficients</a>, signature (16, -112, 448, -1120, 1792, -1792, 1024, -256).
%F G.f.: ((1-x)/(1-2*x))^8.
%F For n > 0, a(n) = 2^(n-12)*(n+9) * (n^6 + 75*n^5 + 1999*n^4 + 23169*n^3 + 115768*n^2 + 232284*n + 142800)/315. - _Bruno Berselli_, Aug 07 2011
%t CoefficientList[Series[((1-x)/(1-2x))^8,{x,0,30}],x] (* _Harvey P. Dale_, Nov 24 2016 *)
%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