%I
%S 1,1,0,0,2,2,5,6,5,3,26,70,141,221,229,18,891,2914,6524,11238,
%T 13690,4214,37619,145018,353534,657080,895234,534007,1654246,
%U 7840402,20737566,41200153,61402057,50500722,68352913,441195837,1272153666,2690651374
%N G.f. A(x) satisfies: A(x)^3 equals the g.f. of A110640, which consists entirely of numbers 1 through 9.
%C A110640 is formed from every third term of A083949, which also consists entirely of numbers 1 through 9.
%F G.f. A(x) satisfies: A(x)^9 (mod 27) = g.f. of A083949.
%e A(x) = 1 + x + 2*x^4  2*x^5 + 5*x^6  6*x^7 + 5*x^8 + 3*x^9 +...
%e A(x)^3 = 1 + 3*x + 3*x^2 + x^3 + 6*x^4 + 6*x^5 + 9*x^6 + 6*x^7 +...
%e A(x)^9 = 1 + 9*x + 36*x^2 + 84*x^3 + 144*x^4 + 252*x^5 + 489*x^6 +..
%e A(x)^9 (mod 27) = 1 + 9*x + 9*x^2 + 3*x^3 + 9*x^4 + 9*x^5 + 3*x^6+..
%e G(x) = 1 + 9*x + 9*x^2 + 3*x^3 + 9*x^4 + 9*x^5 + 3*x^6 + 9*x^7 +...
%e where G(x) is the g.f. of A083949.
%o (PARI) {a(n)=local(d=3,m=9,A=1+m*x); for(j=2,d*n, for(k=1,m,t=polcoeff((A+k*x^j+x*O(x^j))^(1/m),j); if(denominator(t)==1,A=A+k*x^j;break))); polcoeff(Ser(vector(n+1,i,polcoeff(A,d*(i1))))^(1/3),n)}
%Y Cf. A110640, A083949.
%K sign
%O 0,5
%A _Paul D. Hanna_, Sep 14 2005
