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%I #5 Apr 17 2013 19:09:51
%S 1,1,1,2,6,23,110,607,3742,25324,185566,1457998,12195992,108010446,
%T 1008224881,9883048933,101418491070,1086613660608,12126900841444,
%U 140682966122152,1693340044490513,21111988598271746,272228110567491910,3625334790162237116
%N G.f. satisfies: A(x) = Sum_{n>=0} x^n / (A(x) - n*x)^n.
%F G.f. satisfies: A(x) = 1 + G(x/A(x)) where G(x) is the g.f. of A080108, where A080108(n) = Sum_{k=1..n} k^(n-k)*C(n-1,k-1).
%e G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 6*x^4 + 23*x^5 + 110*x^6 + 607*x^7 +...
%e where, by definition,
%e A(x) = 1 + x/(A(x) - x) + x^2/(A(x) - 2*x)^2 + x^3/(A(x) - 3*x)^3 + x^4/(A(x) - 4*x)^4 + x^5/(A(x) - 5*x)^5 +....
%e Also, the g.f. satisfies:
%e A(x) = 1 + x/A(x) + 2*x^2/A(x)^2 + 6*x^3/A(x)^3 + 23*x^4/A(x)^4 + 104*x^5/A(x)^5 + 537*x^6/A(x)^6 +...+ A080108(n)*x^n/A(x)^n +...
%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, x^m/(A-m*x+x*O(x^n))^m)); polcoeff(A, n)}
%o for(n=0, 30, print1(a(n), ", "))
%Y Cf. A211207, A099947, A080108.
%K nonn
%O 0,4
%A _Paul D. Hanna_, Apr 17 2013
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