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%I #7 Aug 24 2017 08:39:56
%S 1,1,8,120,2528,66704,2080128,74115840,2952926720,129637843968,
%T 6205231472640,321275171444736,17880710254829568,1064356462925701120,
%U 67476012302577762304,4539384115900126199808,323034928746773883518976,24248087962137553507450880
%N G.f. satisfies: A(x) = 1 + x*( d/dx x*A(x) )^4.
%H Vaclav Kotesovec, <a href="/A211825/b211825.txt">Table of n, a(n) for n = 0..260</a>
%F G.f. satisfies: A(x) = 1 + x*(A(x) + x*A'(x))^4.
%F a(n) ~ c * 4^n * n! * n^(3/2), where c = 0.06185263969861377609335... - _Vaclav Kotesovec_, Aug 24 2017
%e G.f.: A(x) = 1 + x + 8*x^2 + 120*x^3 + 2528*x^4 + 66704*x^5 + 2080128*x^6 +...
%e Related expansions:
%e d/dx x*A(x) = 1 + 2*x + 24*x^2 + 480*x^3 + 12640*x^4 + 400224*x^5 +...
%e A'(x) = 1 + 16*x + 360*x^2 + 10112*x^3 + 333520*x^4 + 12480768*x^5 +...
%o (PARI) {a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=1+x*deriv(x*A)^4);polcoeff(A,n)}
%o for(n=0,25,print1(a(n),", "))
%Y Cf. A112915, A211824, A211826.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Apr 21 2012
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