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A155806 E.g.f. satisfies: A(x) = Sum_{n>=0} x^n/n! * A(x)^(n^2).

%I A155806 #2 Mar 30 2012 18:37:16
%S A155806 1,1,3,22,269,4616,102847,2824816,92355769,3506278528,151720849691,
%T A155806 7375146930944,398113181435653,23640909385071616,1532325553233566743,
%U A155806 107698939845869111296,8162300091585206125553,663836705760309127184384
%N A155806 E.g.f. satisfies: A(x) = Sum_{n>=0} x^n/n! * A(x)^(n^2).
%F A155806 E.g.f. satisfies: A(x) = B(x/A(x)) and A(x*B(x)) = B(x) where B(x) satisfies:
%F A155806 B(x) = Sum_{n>=0} x^n/n! * B(x)^(n*(n+1)) and is the e.g.f. of A155807.
%e A155806 E.g.f.: A(x) = 1 + x + 3*x^2/2! + 22*x^3/3! + 269*x^4/4! + 4616*x^5/5! +...
%e A155806 where e.g.f. A(x) satisfies:
%e A155806 A(x) = 1 + x*A(x) + x^2/2!*A(x)^4 + x^3/3!*A(x)^9 + x^4/4!*A(x)^16 +...
%e A155806 Let B(x) = A(x*B(x)) be the e.g.f. of A155807 then:
%e A155806 B(x) = 1 + x*B(x)^2 + x^2/2!*B(x)^6 + x^3/3!*B(x)^12 + x^4/4!*B(x)^20 +...
%e A155806 B(x) = 1 + x + 5*x^2/2! + 55*x^3/3! + 969*x^4/4! + 23661*x^5/5! + 741013*x^6/6! +...
%o A155806 (PARI) {a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=1+sum(k=1,n,x^k*A^(k^2)/k!+x*O(x^n))); n!*polcoeff(A,n)}
%Y A155806 Cf. A155804, A155805, A155807.
%K A155806 nonn
%O A155806 0,3
%A A155806 _Paul D. Hanna_, Jan 27 2009