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%I #37 Sep 08 2022 08:45:49
%S 1,7,35,147,553,1925,6321,19825,59906,175504,500864,1397536,3823680,
%T 10282496,27230464,71129856,183518720,468213760,1182433280,2958376960,
%U 7338426368,18059821056,44120473600,107055742976,258122317824,618683957248,1474700509184
%N Expansion of ((1-x)/(1-2*x))^7.
%C a(n) is the number of weak compositions of n with exactly 6 parts equal to 0. - _Milan Janjic_, Jun 27 2010
%H Vincenzo Librandi, <a href="/A169794/b169794.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_07">Index entries for linear recurrences with constant coefficients</a>, signature (14, -84, 280, -560, 672, -448, 128).
%F G.f.: ((1-x)/(1-2*x))^7.
%F For n > 0, a(n) = 2^(n-11)*(n+3)*(n+6)*(n^4 + 54*n^3 + 931*n^2 + 5454*n + 5080)/45. - _Bruno Berselli_, Aug 07 2011
%p seq(coeff(series(((1-x)/(1-2*x))^7,x,n+1), x, n), n = 0 .. 30); # _Muniru A Asiru_, Oct 16 2018
%t CoefficientList[Series[((1 - x)/(1 - 2 x))^7, {x, 0, 26}], x] (* _Michael De Vlieger_, Oct 15 2018 *)
%o (PARI) x='x+O('x^30); Vec(((1-x)/(1-2*x))^7) \\ _G. C. Greubel_, Oct 16 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(((1-x)/(1-2*x))^7)); // _G. C. Greubel_, Oct 16 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
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