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%I #7 Mar 30 2012 18:37:27
%S 1,1,3,18,171,2283,39942,874944,23243829,731486637,26782956144,
%T 1124838704976,53567894139165,2865318598843281,170774893724336223,
%U 11264050942430761881,817374450539598433587,64917115563124199691834
%N E.g.f. A(x) satisfies: A'(x) = 1 + A(A(A(x))).
%e E.g.f.: A(x) = x + x^2/2! + 3*x^3/3! + 18*x^4/4! + 171*x^5/5! + 2283*x^6/6! +...
%e where the derivative of the e.g.f. begins:
%e A'(x) = 1 + x + 3*x^2/2! + 18*x^3/3! + 171*x^4/4! + 2283*x^5/5! +...
%e Related expansions.
%e A(A(x)) = x + 2*x^2/2! + 9*x^3/3! + 69*x^4/4! + 777*x^5/5! + 11802*x^6/6! + 229047*x^7/7! + 5472600*x^8/8! +...
%e A(A(A(x))) = x + 3*x^2/2! + 18*x^3/3! + 171*x^4/4! + 2283*x^5/5! +...
%o (PARI) {a(n)=local(A=x); for(i=1, n, A=intformal(1+subst(A, x, subst(A, x, A+O(x^(n+1)))))); n!*polcoeff(A, n)}
%Y Cf. A001028, A193099, A193100, A179420.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Jul 15 2011
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