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A213105 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^12)^6.

%I A213105 #7 Nov 06 2019 04:25:22
%S A213105 1,1,6,57,614,7716,104322,1529385,23689968,385885521,6531397090,
%T A213105 114147452526,2045979734964,37435147640010,696431496524796,
%U A213105 13134442980269397,250527556214516892,4824098879117797749,93639919777995946446,1830133457257882605430
%N A213105 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^12)^6.
%C A213105 Compare definition of g.f. to:
%C A213105 (1) B(x) = 1 + x/B(-x*B(x)) when B(x) = 1/(1-x).
%C A213105 (2) C(x) = 1 + x/C(-x*C(x)^3)^2 when C(x) = 1 + x*C(x)^2 (A000108).
%C A213105 (3) D(x) = 1 + x/D(-x*D(x)^5)^3 when D(x) = 1 + x*D(x)^3 (A001764).
%C A213105 (4) E(x) = 1 + x/E(-x*E(x)^7)^4 when E(x) = 1 + x*E(x)^4 (A002293).
%C A213105 (5) F(x) = 1 + x/F(-x*F(x)^9)^5 when F(x) = 1 + x*F(x)^5 (A002294).
%C A213105 (6) G(x) = 1 + x/G(-x*G(x)^11)^6 when G(x) = 1 + x*G(x)^6 (A002295).
%e A213105 G.f.: A(x) = 1 + x + 6*x^2 + 57*x^3 + 614*x^4 + 7716*x^5 + 104322*x^6 +...
%e A213105 Related expansions:
%e A213105 A(x)^12 = 1 + 12*x + 138*x^2 + 1696*x^3 + 21723*x^4 + 292836*x^5 +...
%e A213105 A(-x*A(x)^12)^6 = 1 - 6*x - 21*x^2 - 146*x^3 - 1959*x^4 - 25056*x^5 -...
%t A213105 m = 20; A[_] = 1; Do[A[x_] = 1 + x/A[-x A[x]^12]^6 + O[x]^m, {m}];
%t A213105 CoefficientList[A[x], x] (* _Jean-François Alcover_, Nov 06 2019 *)
%o A213105 (PARI) {a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=1+x/subst(A^6,x,-x*subst(A^12,x,x+x*O(x^n))) );polcoeff(A,n)}
%o A213105 for(n=0,30,print1(a(n),", "))
%Y A213105 Cf. A213091, A213092, A213093, A213094, A213095, A213096.
%Y A213105 Cf. A213098, A213099, A213100, A213101, A213102, A213103, A213104.
%K A213105 nonn
%O A213105 0,3
%A A213105 _Paul D. Hanna_, Jun 05 2012