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G.f. satisfies: A(x) = Sum_{n>=0} x^n * (A(x)^n + 1)^n.
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%I #13 Sep 17 2014 07:07:36

%S 1,2,6,30,198,1526,13014,119454,1161094,11828966,125456438,1378837422,

%T 15654724742,183216332886,2207257195798,27347515306814,

%U 348276224255878,4557686850206662,61280403794571894,846507901281129550,12013072624622078854,175127895948991871542

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

%H Vaclav Kotesovec, <a href="/A203000/b203000.txt">Table of n, a(n) for n = 0..150</a>

%F G.f. satisfies: A(x) = Sum_{n>=0} x^n * A(x)^(n^2)/(1 - x*A(x)^n)^(n+1).

%e G.f.: A(x) = 1 + 2*x + 6*x^2 + 30*x^3 + 198*x^4 + 1526*x^5 + 13014*x^6 +...

%e where the g.f. satisfies following series identity:

%e A(x) = 1 + (A(x)+1)*x + (A(x)^2+1)^2*x^2 + (A(x)^3+1)^3*x^3 + (A(x)^4+1)^4*x^4 +...

%e A(x) = 1/(1-x) + x*A(x)/(1-x*A(x))^2 + x^2*A(x)^4/(1-x*A(x)^2)^3 + x^3*A(x)^9/(1-x*A(x)^3)^4 + x^4*A(x)^16/(1-x*A(x)^4)^5 +...

%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=sum(k=0, n, A^(k^2)*x^k/(1-A^k*x+x*O(x^n))^(k+1) ));polcoeff(A, n)}

%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=sum(k=0, n, (A^k+1+x*O(x^n))^k*x^k));polcoeff(A, n)}

%Y Cf. A247330, A203014, A186998, A186999.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Dec 27 2011