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G.f. satisfies: A(x) = Sum_{n>=0} x^n/(1 - x*A(x)^n)^n.
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%I #10 Dec 26 2022 08:34:00

%S 1,1,2,5,16,60,248,1098,5127,24996,126353,658914,3531891,19406185,

%T 109079066,626240743,3668020847,21899151005,133179027307,824588095681,

%U 5195945625141,33311336524674,217230789307751,1440698723164953

%N G.f. satisfies: A(x) = Sum_{n>=0} x^n/(1 - x*A(x)^n)^n.

%H Paul D. Hanna, <a href="/A186999/b186999.txt">Table of n, a(n) for n = 0..200</a>

%e G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 60*x^5 + 248*x^6 +...

%e The g.f. satisfies:

%e A(x) = 1 + x/(1-x*A(x)) + x^2/(1-x*A(x)^2)^2 + x^3/(1-x*A(x)^3)^3 +...

%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m/(1-x*(A+x*O(x^n))^m)^m));polcoeff(A,n)}

%Y Cf. A203000, A186998.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Mar 01 2011