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A213229 G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^7)^2).

%I A213229 #6 Aug 16 2024 17:42:29
%S A213229 1,1,3,16,93,649,4924,40221,344817,3058115,27798895,257009431,
%T A213229 2404734586,22679499148,214947515333,2042353663088,19417906390395,
%U A213229 184458621283607,1748712359825873,16530801697256737,155736745914813741,1461877902947680987,13674142992787617967
%N A213229 G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^7)^2).
%C A213229 Compare g.f. to:
%C A213229 (1) G(x) = 1/(1 - x/G(-x*G(x)^3)^1) when G(x) = 1/(1 - x*G(x)^1) (A000108).
%C A213229 (2) G(x) = 1/(1 - x/G(-x*G(x)^5)^2) when G(x) = 1/(1 - x*G(x)^2) (A001764).
%C A213229 (3) G(x) = 1/(1 - x/G(-x*G(x)^7)^3) when G(x) = 1/(1 - x*G(x)^3) (A002293).
%C A213229 (4) G(x) = 1/(1 - x/G(-x*G(x)^9)^4) when G(x) = 1/(1 - x*G(x)^4) (A002294).
%e A213229 G.f.: A(x) = 1 + x + 3*x^2 + 16*x^3 + 93*x^4 + 649*x^5 + 4924*x^6 +...
%e A213229 Related expansions:
%e A213229 A(x)^7 = 1 + 7*x + 42*x^2 + 273*x^3 + 1862*x^4 + 13531*x^5 + 104062*x^6 +...
%e A213229 1/A(-x*A(x)^7)^2 = 1 + 2*x + 11*x^2 + 60*x^3 + 431*x^4 + 3302*x^5 + 27421*x^6 +..
%o A213229 (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^7, x, x+x*O(x^n)))) ); polcoeff(A, n)}
%o A213229 for(n=0, 30, print1(a(n), ", "))
%Y A213229 Cf. A213225, A213226, A213227, A213228, A213230, A213231, A213232, A213233.
%Y A213229 Cf. A213091, A213092, A213093, A213094, A213095, A213096, A213098.
%Y A213229 Cf. A213099, A213100, A213101, A213102, A213103, A213104, A213105.
%Y A213229 Cf. A213108, A213109, A213110, A213111, A213112, A213113.
%K A213229 nonn
%O A213229 0,3
%A A213229 _Paul D. Hanna_, Jun 06 2012