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%I #5 Mar 30 2012 18:37:27
%S 1,1,2,11,142,3394,128368,7003110,518966378,50079318914,6097188090560,
%T 913799530877734,165277883587449772,35492379675559089096,
%U 8926289062300717394696,2598758767007565055432545,867087614897934091698944876
%N G.f. satisfies: A(A(x)) = Sum_{n>=1} a(n)*x^n * (1 + n*x)^n, where g.f. A(x) = Sum_{n>=1} a(n)*x^n.
%e G.f.: A(x) = x + x^2 + 2*x^3 + 11*x^4 + 142*x^5 + 3394*x^6 +...
%e where
%e A(A(x)) = x*(1+x) + x^2*(1+2*x)^2 + 2*x^3*(1+3*x)^3 + 11*x^4*(1+4*x)^4 + 142*x^5*(1+5*x)^5 + 3394*x^6*(1+6*x)^6 +...+ a(n)*x^n*(1+n*x)^n +...
%e Explicitly,
%e A(A(x)) = x + 2*x^2 + 6*x^3 + 33*x^4 + 372*x^5 + 8054*x^6 + 288868*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+m*x +x*O(x^#A))^m );
%o A[#A]=Vec(G)[#A]-Vec(subst(F,x,F))[#A]);if(n<1,0,A[n])}
%Y Cf. A193210.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Jul 19 2011
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