%I #7 Sep 19 2013 17:57:01
%S 1,1,2,6,27,172,1508,18107,297532,6694132,206841391,8816277300,
%T 520844677834,42854370882379,4933351077116176,797908056582772334,
%U 181972606629594221271,58701383528452842764544,26853636463946258949427440,17457976736153040916394583563
%N G.f. satisfies: A(x) = Sum{n>=0} A( n*x/(1-n*x) ) * x^n, with A(0)=1.
%F G.f.: Sum_{n>=0} x^n * Sum{k=0..n} a(k)*(n-k)^k/(1 - (n-k)*x)^k = Sum_{n>=0} a(n)*x^n.
%e G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 27*x^4 + 172*x^5 + 1508*x^6 +...
%e where
%e A(x) = 1 + A(x/(1-x))*x + A(2*x/(1-2*x))*x^2 + A(3*x/(1-3*x))*x^3 + A(4*x/(1-4*x))*x^4 + A(5*x/(1-5*x))*x^5 +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=sum(m=0,n,subst(A,x,m*x/(1-m*x+x*O(x^n)))*x^m));polcoeff(A,n)}
%o for(n=0,21,print1(a(n),", "))
%Y Cf. A125282.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Sep 19 2013