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A213230 G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^8)^2).

%I A213230 #6 Aug 16 2024 18:47:35
%S A213230 1,1,3,18,115,902,7722,70784,678251,6670586,66851992,677328214,
%T A213230 6903177354,70490174298,718856047396,7304677030708,73837797474235,
%U A213230 741722190452840,7402780597473820,73459355234486763,726095774886910232,7170907377415662763,71063833561266044578
%N A213230 G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^8)^2).
%C A213230 Compare g.f. to:
%C A213230 (1) G(x) = 1/(1 - x/G(-x*G(x)^3)^1) when G(x) = 1/(1 - x*G(x)^1) (A000108).
%C A213230 (2) G(x) = 1/(1 - x/G(-x*G(x)^5)^2) when G(x) = 1/(1 - x*G(x)^2) (A001764).
%C A213230 (3) G(x) = 1/(1 - x/G(-x*G(x)^7)^3) when G(x) = 1/(1 - x*G(x)^3) (A002293).
%C A213230 (4) G(x) = 1/(1 - x/G(-x*G(x)^9)^4) when G(x) = 1/(1 - x*G(x)^4) (A002294).
%e A213230 G.f.: A(x) = 1 + x + 3*x^2 + 18*x^3 + 115*x^4 + 902*x^5 + 7722*x^6 +...
%e A213230 Related expansions:
%e A213230 A(x)^8 = 1 + 8*x + 52*x^2 + 368*x^3 + 2754*x^4 + 22112*x^5 + 189344*x^6 +...
%e A213230 1/A(-x*A(x)^8)^2 = 1 + 2*x + 13*x^2 + 78*x^3 + 634*x^4 + 5488*x^5 + 50969*x^6 +...
%o A213230 (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1/(1-x/subst(A^2, x, -x*subst(A^8, x, x+x*O(x^n)))) ); polcoeff(A, n)}
%o A213230 for(n=0, 30, print1(a(n), ", "))
%Y A213230 Cf. A213225, A213226, A213227, A213228, A213229, A213231, A213232, A213233.
%Y A213230 Cf. A213091, A213092, A213093, A213094, A213095, A213096, A213098.
%Y A213230 Cf. A213099, A213100, A213101, A213102, A213103, A213104, A213105.
%Y A213230 Cf. A213108, A213109, A213110, A213111, A213112, A213113.
%K A213230 nonn
%O A213230 0,3
%A A213230 _Paul D. Hanna_, Jun 06 2012