%I #7 Nov 23 2018 17:28:54
%S 0,3,5,20,54,169,499,1506,4508,13535,40593,121792,365362,1096101,
%T 3288287,9864878,29594616,88783867,266351581,799054764,2397164270,
%U 7191492833,21574478475,64723435450,194170306324,582510918999
%N Expansion of x^2(3+2x)/(1-x-5x^2-3x^3).
%C Let b(1)=x, b(2)=y, k*b(k)=(2k-1)*b(k-1) + 3(k+1)*b(k-2); then b(n)=c(n)*x+a(n)/3*y.
%F a(1)=0; a(n+1) = 3*a(n)-(-1)^n*(n+2); a(n)=floor((11/48)*3^n+(-1)^n*n/4+1/2)
%t CoefficientList[Series[x^2(3+2x)/(1-x-5x^2-3x^3),{x,0,30}],x] (* _Harvey P. Dale_, Nov 23 2018 *)
%o (PARI) a(n)=if(n<0,0,polcoeff(x^2*(3+2*x)/(1-x-5*x^2-3*x^3)+x*O(x^n),n))
%K nonn
%O 1,2
%A _Benoit Cloitre_, Nov 02 2002