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%I
%S 1,1,0,3,0,3,9,1,18,9,36,45,57,90,114,351,165,558,738,1044,1791,1908,
%T 3915,4926,8568,8553,17217,26271,30474,50967,68526,113319,144324,
%U 219195,299359,473454,665424,860733,1396350,1895913,2762550,3790935,5695974
%N G.f.: A(x) = 1 + x*(A_2)^3; A_2 = 1 + x^2*(A_3)^3; A_3 = 1 + x^3*(A_4)^3; ... A_n = 1 + x^n*(A_{n+1})^3 for n>=1 with A_1 = A(x).
%F G.f. A(x) = B(x,x), where B(w,x) satisfies the functional equation B(w,x) = 1 + x*B(w,wx)^3. B(w,x) is the g.f. for the number of ternary trees of given path length and number of nodes; B(1,x) is the g.f. for A001764.
%o (PARI) {a(n)=local(A=1+x*O(x^n)); for(j=0,n-1,A=1+x^(n-j)*A^3);polcoeff(A,n)}
%Y Cf. A132331 (cube); A001764; A108643 (variant).
%K nonn
%O 0,4
%A _Paul D. Hanna_, Aug 20 2007
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