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A213232 G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^9)^3).

%I A213232 #6 Aug 16 2024 18:54:06
%S A213232 1,1,4,28,215,1983,19789,213698,2426851,28661509,348287354,4322627557,
%T A213232 54508747790,695534616050,8953637420349,116002300640637,
%U A213232 1509724588732027,19707310304585212,257698683361191598,3372154116182404890,44121356408759264549
%N A213232 G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^9)^3).
%C A213232 Compare g.f. to:
%C A213232 (1) G(x) = 1/(1 - x/G(-x*G(x)^3)^1) when G(x) = 1/(1 - x*G(x)^1) (A000108).
%C A213232 (2) G(x) = 1/(1 - x/G(-x*G(x)^5)^2) when G(x) = 1/(1 - x*G(x)^2) (A001764).
%C A213232 (3) G(x) = 1/(1 - x/G(-x*G(x)^7)^3) when G(x) = 1/(1 - x*G(x)^3) (A002293).
%C A213232 (4) G(x) = 1/(1 - x/G(-x*G(x)^9)^4) when G(x) = 1/(1 - x*G(x)^4) (A002294).
%e A213232 G.f.: A(x) = 1 + x + 4*x^2 + 28*x^3 + 215*x^4 + 1983*x^5 + 19789*x^6 +...
%e A213232 Related expansions:
%e A213232 A(x)^9 = 1 + 9*x + 72*x^2 + 624*x^3 + 5661*x^4 + 54621*x^5 + 555837*x^6 +...
%e A213232 1/A(-x*A(x)^9)^3 = 1 + 3*x + 21*x^2 + 154*x^3 + 1446*x^4 + 14511*x^5 + 158838*x^6 +...
%o A213232 (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1/(1-x/subst(A^3, x, -x*subst(A^9, x, x+x*O(x^n)))) ); polcoeff(A, n)}
%o A213232 for(n=0, 30, print1(a(n), ", "))
%Y A213232 Cf. A213225, A213226, A213227, A213228, A213229, A213230, A213231, A213233.
%Y A213232 Cf. A213091, A213092, A213093, A213094, A213095, A213096, A213098.
%Y A213232 Cf. A213099, A213100, A213101, A213102, A213103, A213104, A213105.
%Y A213232 Cf. A213108, A213109, A213110, A213111, A213112, A213113.
%K A213232 nonn
%O A213232 0,3
%A A213232 _Paul D. Hanna_, Jun 06 2012