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%I #7 Mar 30 2012 18:37:27
%S 1,1,2,13,184,4725,188596,10765407,829780846,82924007284,
%T 10420182259194,1607406366386249,298555458341808338,
%U 65711158773953092780,16910051487116790543954,5030141451818448773854244,1712632076858599057432066794
%N G.f. satisfies: A(A(x)) = Sum_{n>=1} a(n)*x^n * (1+x)^(n^2), where g.f. A(x) = Sum_{n>=1} a(n)*x^n.
%e G.f.: A(x) = x + x^2 + 2*x^3 + 13*x^4 + 184*x^5 + 4725*x^6 +...
%e where
%e A(A(x)) = x*(1+x) + x^2*(1+x)^4 + 2*x^3*(1+x)^9 + 13*x^4*(1+x)^16 + 184*x^5*(1+x)^25 + 4725*x^6*(1+x)^36 +...+ a(n)*x^n*(1+x)^(n^2) +...
%e Explicitly,
%e A(A(x)) = x + 2*x^2 + 6*x^3 + 37*x^4 + 468*x^5 + 11054*x^6 + 421428*x^7 +...
%o (PARI) {a(n)=local(A=[1],F=x,G=x);for(i=1,n,A=concat(A,0);F=x*Ser(A);
%o G=sum(m=1,#A-1,A[m]*x^m*(1+x+x*O(x^#A))^(m^2));
%o A[#A]=Vec(G)[#A]-Vec(subst(F,x,F))[#A]);if(n<1,0,A[n])}
%Y Cf. A193193, A193194, A193195.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Jul 19 2011
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