%I #18 Feb 13 2022 11:06:20
%S 0,0,0,1,1,5,9,18,34,58,100,164,265,421,657,1015,1549,2343,3515,5234,
%T 7745,11393,16673,24285,35220,50880,73238,105073,150286,214346,304910,
%U 432677,612581,865435,1220209,1717180,2412276,3383076,4737076,6623076,9246855
%N Expansion of x^3*(1+x+2*x^2+3*x^3+3*x^4+x^5)/(1-x^2-x^3)^3.
%H Harvey P. Dale, <a href="/A257595/b257595.txt">Table of n, a(n) for n = 0..1000</a>
%H Jean-Luc Baril, and Jean-Marcel Pallo, <a href="http://jl.baril.u-bourgogne.fr/filter.pdf">A Motzkin filter in the Tamari lattice</a>, Discrete Mathematics 338.8 (2015): 1370-1378.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,3,-3,-6,-2,3,3,1 ).
%F G.f.: x^3*(1+x+2*x^2+3*x^3+3*x^4+x^5)/(1-x^2-x^3)^3.
%t CoefficientList[Series[x^3(1+x+2x^2+3x^3+3x^4+x^5)/(1-x^2-x^3)^3,{x,0,50}],x] (* or *) LinearRecurrence[{0,3,3,-3,-6,-2,3,3,1},{0,0,0,1,1,5,9,18,34},50] (* _Harvey P. Dale_, Feb 13 2022 *)
%K nonn,easy
%O 0,6
%A _N. J. A. Sloane_, Jun 04 2015
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