A193210 - OEIS

%I #5 Mar 30 2012 18:37:27

%S 1,1,3,24,393,11043,473041,28601334,2315263942,241478700774,

%T 31517159612387,5030510468876181,963773726037574349,

%U 218238081089074417113,57654070089428439591645,17573072391553388287162662,6120849041684563565434585529

%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 + 3*x^3 + 24*x^4 + 393*x^5 + 11043*x^6 +...

%e where

%e A(A(x)) = x/(1-x) + x^2/(1-2*x)^2 + 3*x^3/(1-3*x)^3 + 24*x^4/(1-4*x)^4 + 393*x^5/(1-5*x)^5 + 11043*x^6/(1-6*x)^6 +...+ a(n)*x^n/(1-n*x)^n +...

%e Explicitly,

%e A(A(x)) = x + 2*x^2 + 8*x^3 + 64*x^4 + 972*x^5 + 25599*x^6 +...

%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. A193209.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Jul 19 2011