cp's OEIS Frontend

A213101 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^8)^4.

%I A213101 #13 Nov 06 2019 04:21:51
%S A213101 1,1,4,26,188,1627,15172,154904,1670836,18951217,222682164,2693625128,
%T A213101 33309537808,419311915217,5354144473084,69169422070152,
%U A213101 902237854706616,11863641066687085,157052133090437332,2090929291636792824,27971914781646817864,375725009230868446500
%N A213101 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^8)^4.
%C A213101 Compare definition of g.f. to:
%C A213101 (1) B(x) = 1 + x/B(-x*B(x)) when B(x) = 1/(1-x).
%C A213101 (2) C(x) = 1 + x/C(-x*C(x)^3)^2 when C(x) = 1 + x*C(x)^2 (A000108).
%C A213101 (3) D(x) = 1 + x/D(-x*D(x)^5)^3 when D(x) = 1 + x*D(x)^3 (A001764).
%C A213101 (4) E(x) = 1 + x/E(-x*E(x)^7)^4 when E(x) = 1 + x*E(x)^4 (A002293).
%C A213101 (5) F(x) = 1 + x/F(-x*F(x)^9)^5 when F(x) = 1 + x*F(x)^5 (A002294).
%C A213101 The first negative term is a(249). - _Georg Fischer_, Feb 16 2019
%H A213101 Paul D. Hanna, <a href="/A213101/b213101.txt">Table of n, a(n) for n = 0..300</a>
%e A213101 G.f.: A(x) = 1 + x + 4*x^2 + 26*x^3 + 188*x^4 + 1627*x^5 + 15172*x^6 +...
%e A213101 Related expansions:
%e A213101 A(x)^8 = 1 + 8*x + 60*x^2 + 488*x^3 + 4150*x^4 + 37600*x^5 + 358788*x^6 +...
%e A213101 A(-x*A(x)^8)^4 = 1 - 4*x - 10*x^2 - 44*x^3 - 439*x^4 - 3884*x^5 - 42724*x^6 -...
%t A213101 m = 22; A[_] = 1; Do[A[x_] = 1 + x/A[-x A[x]^8]^4 + O[x]^m, {m}];
%t A213101 CoefficientList[A[x], x] (* _Jean-François Alcover_, Nov 06 2019 *)
%o A213101 (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^8,x,x+x*O(x^n))) );polcoeff(A,n)}
%o A213101 for(n=0,30,print1(a(n),", "))
%Y A213101 Cf. A000108, A001764, A002293, A002294, A213091, A213092, A213093, A213094, A213095, A213096, A213098, A213099, A213100, A213102, A213103, A213104, A213105.
%K A213101 sign
%O A213101 0,3
%A A213101 _Paul D. Hanna_, Jun 05 2012