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A213104 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^10)^5.

%I A213104 #16 Nov 06 2019 04:22:05
%S A213104 1,1,5,40,360,3820,43651,543240,7146185,98885725,1420274645,
%T A213104 21037156031,319127602075,4935547265370,77525696636995,
%U A213104 1233356748777015,19829269320322346,321631227310756885,5255920261950786655,86436636022328320125,1429253483704685851315
%N A213104 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^10)^5.
%C A213104 Compare definition of g.f. to:
%C A213104 (1) B(x) = 1 + x/B(-x*B(x)) when B(x) = 1/(1-x).
%C A213104 (2) C(x) = 1 + x/C(-x*C(x)^3)^2 when C(x) = 1 + x*C(x)^2 (A000108).
%C A213104 (3) D(x) = 1 + x/D(-x*D(x)^5)^3 when D(x) = 1 + x*D(x)^3 (A001764).
%C A213104 (4) E(x) = 1 + x/E(-x*E(x)^7)^4 when E(x) = 1 + x*E(x)^4 (A002293).
%C A213104 (5) F(x) = 1 + x/F(-x*F(x)^9)^5 when F(x) = 1 + x*F(x)^5 (A002294).
%C A213104 (6) G(x) = 1 + x/G(-x*G(x)^11)^6 when G(x) = 1 + x*G(x)^6 (A002295).
%C A213104 The first negative term is a(306). - _Georg Fischer_, Feb 16 2019
%H A213104 Paul D. Hanna, <a href="/A213104/b213104.txt">Table of n, a(n) for n = 0..400</a>
%e A213104 G.f.: A(x) = 1 + x + 5*x^2 + 40*x^3 + 360*x^4 + 3820*x^5 + 43651*x^6 +...
%e A213104 Related expansions:
%e A213104 A(x)^10 = 1 + 10*x + 95*x^2 + 970*x^3 + 10335*x^4 + 116452*x^5 +...
%e A213104 A(-x*A(x)^10)^5 = 1 - 5*x - 15*x^2 - 85*x^3 - 995*x^4 - 10776*x^5 -...
%t A213104 m = 21; A[_] = 1; Do[A[x_] = 1 + x/A[-x A[x]^10]^5 + O[x]^m, {m}];
%t A213104 CoefficientList[A[x], x] (* _Jean-François Alcover_, Nov 06 2019 *)
%o A213104 (PARI) {a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=1+x/subst(A^5,x,-x*subst(A^10,x,x+x*O(x^n))) );polcoeff(A,n)}
%o A213104 for(n=0,30,print1(a(n),", "))
%Y A213104 Cf. A000108, A001764, A002293, A002294, A002295, A213091, A213092, A213093, A213094, A213095, A213096, A213098, A213099, A213100, A213101, A213102, A213103, A213105.
%K A213104 sign
%O A213104 0,3
%A A213104 _Paul D. Hanna_, Jun 05 2012