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A213103 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^12)^4.

%I A213103 #15 Nov 06 2019 04:21:20
%S A213103 1,1,4,42,420,5779,83104,1306684,21283504,356648125,6100611232,
%T A213103 105634585546,1845124077000,32368064972555,568794055227200,
%U A213103 9991239094888864,175142529040285920,3060545399532144497,53279047286232892928,923884653765128839312,15965368274611453269820
%N A213103 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^12)^4.
%C A213103 Compare definition of g.f. to:
%C A213103 (1) B(x) = 1 + x/B(-x*B(x)) when B(x) = 1/(1-x).
%C A213103 (2) C(x) = 1 + x/C(-x*C(x)^3)^2 when C(x) = 1 + x*C(x)^2 (A000108).
%C A213103 (3) D(x) = 1 + x/D(-x*D(x)^5)^3 when D(x) = 1 + x*D(x)^3 (A001764).
%C A213103 (4) E(x) = 1 + x/E(-x*E(x)^7)^4 when E(x) = 1 + x*E(x)^4 (A002293).
%C A213103 (5) F(x) = 1 + x/F(-x*F(x)^9)^5 when F(x) = 1 + x*F(x)^5 (A002294).
%C A213103 The first negative term is a(76). - _Georg Fischer_, Feb 16 2019
%H A213103 Paul D. Hanna, <a href="/A213103/b213103.txt">Table of n, a(n) for n = 0..300</a>
%e A213103 G.f.: A(x) = 1 + x + 4*x^2 + 42*x^3 + 420*x^4 + 5779*x^5 + 83104*x^6 +...
%e A213103 Related expansions:
%e A213103 A(x)^12 = 1 + 12*x + 114*x^2 + 1252*x^3 + 14775*x^4 + 193956*x^5 +...
%e A213103 A(-x*A(x)^12)^4 = 1 - 4*x - 26*x^2 - 148*x^3 - 2415*x^4 - 33192*x^5 -...
%t A213103 m = 21; A[_] = 1; Do[A[x_] = 1 + x/A[-x A[x]^12]^4 + O[x]^m, {m}];
%t A213103 CoefficientList[A[x], x] (* _Jean-François Alcover_, Nov 06 2019 *)
%o A213103 (PARI) {a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=1+x/subst(A^4,x,-x*subst(A^12,x,x+x*O(x^n))) );polcoeff(A,n)}
%o A213103 for(n=0,30,print1(a(n),", "))
%Y A213103 Cf. A000108, A001764, A002293, A002294, A213091, A213092, A213093, A213094, A213095, A213096, A213098, A213099, A213100, A213101, A213102, A213104, A213105.
%K A213103 sign
%O A213103 0,3
%A A213103 _Paul D. Hanna_, Jun 05 2012