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%I #9 Feb 24 2014 17:58:11
%S 1,1,1,4,15,64,355,2424,17521,145280,1360521,13884320,153669791,
%T 1856114688,24118429595,335060591488,4969674145185,78372603670528,
%U 1307723372124625,23033289496343040,427152897455369455,8316956600840806400,169633856906699985555,3617390574964855445504,80494223066221543513745
%N E.g.f. satisfies: A(x) = exp( Integral (1 + x*A(x) + x^2*A(x)^2)/A(x) dx ).
%C Compare to: G(x) = exp( Integral (1 + 2*x*G(x) + x^2*G(x)^2)/G(x) dx ) holds when G(x) = 1/(1-x).
%H Vaclav Kotesovec, <a href="/A233536/b233536.txt">Table of n, a(n) for n = 0..300</a>
%F E.g.f. satisfies: A'(x) = (1 - x^3*A(x)^3) / (1 - x*A(x)).
%F a(n) ~ n! * d^(n+3), where d = 0.9271503577507272... - _Vaclav Kotesovec_, Feb 24 2014
%e E.g.f.: A(x) = 1 + x + x^2/2! + 4*x^3/3! + 15*x^4/4! + 64*x^5/5! + 355*x^6/6! +...
%e Related expansions:
%e A'(x) = 1 + x*A(x) + x^2*A(x)^2 = 1 + x + 4*x^2/2! + 15*x^3/3! + 64*x^4/4! + 355*x^5/5! + 2424*x^6/6! + 17521*x^7/7! +...
%e (1 + x*A(x) + x^2*A(x)^2)/A(x) = 1 + 3*x^2/2! + 2*x^3/3! + 23*x^4/4! + 36*x^5/5! + 673*x^6/6! + 1328*x^7/7! +...
%e log(A(x)) = x + 3*x^3/3! + 2*x^4/4! + 23*x^5/5! + 36*x^6/6! + 673*x^7/7! +...
%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(intformal((1+x*A+x^2*A^2)/A+x*O(x^n)))); n!*polcoeff(A, n)}
%o for(n=0, 30, print1(a(n), ", "))
%K nonn
%O 0,4
%A _Paul D. Hanna_, Dec 14 2013
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