%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