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A218224 G.f. A(x) satisfies: A(x) = 1+x + x^2*[d/dx A(x)^4].

%I A218224 #6 Aug 24 2017 09:00:30
%S A218224 1,1,4,44,684,13636,328000,9198240,294075040,10549834368,419626384128,
%T A218224 18330935118080,872618259925632,44970631837229184,2494887017741434368,
%U A218224 148272655438005392896,9399158287979230003200,633107847492164526284800,45159576693655485274008576
%N A218224 G.f. A(x) satisfies: A(x) = 1+x + x^2*[d/dx A(x)^4].
%H A218224 Vaclav Kotesovec, <a href="/A218224/b218224.txt">Table of n, a(n) for n = 0..330</a>
%F A218224 G.f. A(x) satisfies: A(x) = 1+x + 4*x^2*A(x)^3*A'(x).
%F A218224 a(n) ~ c * 4^n * n! / n^(1/4), where c = 0.2277218505566340305314... - _Vaclav Kotesovec_, Aug 24 2017
%e A218224 G.f.: A(x) = 1 + x + 4*x^2 + 44*x^3 + 684*x^4 + 13636*x^5 + 328000*x^6 +...
%e A218224 Related series:
%e A218224 A(x)^3 = 1 + 4*x + 22*x^2 + 228*x^3 + 3409*x^4 + 65600*x^5 + 1533040*x^6 +...
%e A218224 d/dx A(x)^3 = 4 + 44*x + 684*x^2 + 13636*x^3 + 328000*x^4 + 9198240*x^5 +...
%o A218224 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x+x^2*deriv(A^4+x*O(x^n))); polcoeff(A, n)}
%o A218224 for(n=0, 30, print1(a(n), ", "))
%Y A218224 Cf. A185183, A218223.
%K A218224 nonn
%O A218224 0,3
%A A218224 _Paul D. Hanna_, Oct 23 2012