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%I #2 Mar 30 2012 18:37:17
%S 1,2,6,20,69,245,885,3235,11923,44211,164694,615721,2308499,8675121,
%T 32661637,123161206,465018949,1757672820,6649722003,25177228890,
%U 95390000028,361616383623,1371545371027,5204283449684,19754979558587
%N G.f. A(x) equals an infinite symmetric composition of functions x/(1-x^n), n=1,2,3,...
%C Limit a(n+1)/a(n) ~ 3.80825961708875...
%F G.f.: A(x) = x/(1-x) o x/(1-x^2) o x/(1-x^3) o...o (x) o...o x/(1-x^3) o x/(1-x^2) o x/(1-x).
%e G.f.: A(x) = x + 2*x^2 + 6*x^3 + 20*x^4 + 69*x^5 + 245*x^6 +...
%e A(x) is the limit of the compositions beginning in the following manner:
%e (1) x/(1-x) o x/(1-x) = x/(1-2*x);
%e (2) x/(1-x) o x/(1-x^2) o x/(1-x^2) o x/(1-x) = (x-3*x^2+2*x^3)/(1-5*x+6*x^2-x^4);
%e (3) x/(1-x) o x/(1-x^2) o x/(1-x^3) o x/(1-x^3) o x/(1-x^2) o x/(1-x); ...
%o (PARI) {a(n)=local(F=x); if(n<1, 0, for(k=1, n, F=subst(subst(x/(1-x^(n-k+1)),x,F),x,x/(1-x^(n-k+1) +x*O(x^n)));); return(polcoeff(F, n)))}
%Y Cf. A163134.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Aug 12 2009
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