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A169797 Expansion of ((1-x)/(1-2x))^10.

%I A169797 #32 Oct 15 2018 22:15:58
%S A169797 1,10,65,340,1550,6412,24650,89440,309605,1030490,3317445,10377180,
%T A169797 31655820,94451520,276313200,794169792,2246410560,6262748160,
%U A169797 17230138880,46831339520,125870737408,334826700800,882159984640,2303540756480,5965195018240,15327324667904
%N A169797 Expansion of ((1-x)/(1-2x))^10.
%C A169797 a(n) is the number of weak compositions of n with exactly 9 parts equal to 0. - _Milan Janjic_, Jun 27 2010
%H A169797 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 A169797 M. Janjic and B. Petkovic, <a href="http://arxiv.org/abs/1301.4550">A Counting Function</a>, arXiv 1301.4550 [math.CO], 2013.
%H A169797 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 A169797 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (20,-180,960,-3360,8064,-13440,15360,-11520,5120,-1024)
%F A169797 a(n) = 2^(n-17)*(n+11) *(n^8 + 124*n^7 + 5986*n^6 + 143944*n^5 + 1836529*n^4 + 12358156*n^3 + 42005484*n^2 + 64730736*n + 33747840)/2835, n > 0. - _R. J. Mathar_, Mar 14 2011
%t A169797 CoefficientList[Series[((1-x)/(1-2x))^10,{x,0,30}],x] (* or *) Join[ {1}, LinearRecurrence[{20,-180,960,-3360,8064,-13440,15360,-11520,5120,-1024},{10,65,340,1550,6412,24650,89440,309605,1030490,3317445},30]] (* _Harvey P. Dale_, Aug 21 2014 *)
%o A169797 (PARI) Vec(((1-x)/(1-2*x))^10+O(x^99)) \\ _Charles R Greathouse IV_, Sep 23 2012
%Y A169797 ((1-x)/(1-2x))^k: A011782, A045623, A058396, A062109, A169792-A169797; a row of A160232.
%K A169797 nonn,easy
%O A169797 0,2
%A A169797 _N. J. A. Sloane_, May 15 2010