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%I #2 Mar 30 2012 18:37:17
%S 1,2,6,20,71,266,1033,4133,16919,70543,298461,1277895,5525308,
%T 24086364,105730896,466907516,2072662801,9243364577,41392064353,
%U 186040133239,838962247305,3794801298127,17211872676042,78262816746849
%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) seems to exist, approximately = 4.75...
%F A(x) = ...o x/(1-x^3) o x/(1-x^2) o x/(1-x) o (x) o x/(1-x) o x/(1-x^2) o x/(1-x^3) o...
%e G.f.: A(x) = x + 2*x^2 + 6*x^3 + 20*x^4 + 71*x^5 + 266*x^6 +...
%e A(x) is the limit of compositions beginning in the following manner:
%e (1) x/(1-x) o x/(1-x) = x/(1-2*x);
%e (2) x/(1-x^2) o x/(1-x) o x/(1-x) o x/(1-x^2) = (x-2*x^2-x^3)/(1-4*x+x^2+4*x^3+x^4);
%e (3) x/(1-x^3) o x/(1-x^2) o x/(1-x) o x/(1-x) o x/(1-x^2) o x/(1-x^3); ...
%o (PARI) {a(n)=local(F=x); if(n<1, 0, for(k=1, n, F=subst(subst(x/(1-x^k),x,F),x,x/(1-x^k +x*O(x^n)));); return(polcoeff(F, n)))}
%Y Cf. A163135.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Aug 12 2009
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