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A213228 G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^6)^2).

%I A213228 #6 Aug 16 2024 18:48:44
%S A213228 1,1,3,14,73,440,2862,19991,146939,1125413,8896018,72067978,595097838,
%T A213228 4987609871,42290465703,361845473658,3117830204185,27009650432888,
%U A213228 234932107635587,2049479335366836,17915253987741538,156799716352350344,1373180896765862962
%N A213228 G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^6)^2).
%C A213228 Compare g.f. to:
%C A213228 (1) G(x) = 1/(1 - x/G(-x*G(x)^3)^1) when G(x) = 1/(1 - x*G(x)^1) (A000108).
%C A213228 (2) G(x) = 1/(1 - x/G(-x*G(x)^5)^2) when G(x) = 1/(1 - x*G(x)^2) (A001764).
%C A213228 (3) G(x) = 1/(1 - x/G(-x*G(x)^7)^3) when G(x) = 1/(1 - x*G(x)^3) (A002293).
%C A213228 (4) G(x) = 1/(1 - x/G(-x*G(x)^9)^4) when G(x) = 1/(1 - x*G(x)^4) (A002294).
%e A213228 G.f.: A(x) = 1 + x + 3*x^2 + 14*x^3 + 73*x^4 + 440*x^5 + 2862*x^6 +...
%e A213228 Related expansions:
%e A213228 A(x)^6 = 1 + 6*x + 33*x^2 + 194*x^3 + 1188*x^4 + 7656*x^5 + 51583*x^6 +...
%e A213228 1/A(-x*A(x)^6)^2 = 1 + 2*x + 9*x^2 + 44*x^3 + 268*x^4 + 1750*x^5 + 12422*x^6 +...
%o A213228 (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^6, x, x+x*O(x^n)))) ); polcoeff(A, n)}
%o A213228 for(n=0, 30, print1(a(n), ", "))
%Y A213228 Cf. A213225, A213226, A213227, A213229, A213230, A213231, A213232, A213233.
%Y A213228 Cf. A213091, A213092, A213093, A213094, A213095, A213096, A213098.
%Y A213228 Cf. A213099, A213100, A213101, A213102, A213103, A213104, A213105.
%Y A213228 Cf. A213108, A213109, A213110, A213111, A213112, A213113.
%K A213228 nonn
%O A213228 0,3
%A A213228 _Paul D. Hanna_, Jun 06 2012