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A155807 E.g.f. satisfies: A(x) = Sum_{n>=0} x^n/n! * A(x)^(n(n+1)).

%I A155807 #2 Mar 30 2012 18:37:16
%S A155807 1,1,5,55,969,23661,741013,28363707,1284098609,67149601273,
%T A155807 3984121444581,264485848799679,19426332734137849,1564277403496216293,
%U A155807 137040382838351173301,12977244383702330201731
%N A155807 E.g.f. satisfies: A(x) = Sum_{n>=0} x^n/n! * A(x)^(n(n+1)).
%F A155807 E.g.f. satisfies: A(x) = B(x*A(x)) and A(x/B(x)) = B(x) where B(x) satisfies:
%F A155807 B(x) = Sum_{n>=0} x^n/n! * B(x)^(n^2) and is the e.g.f. of A155806.
%e A155807 E.g.f.: A(x) = 1 + x + 5*x^2/2! + 55*x^3/3! + 969*x^4/4! + 23661*x^5/5! +...
%e A155807 where e.g.f. A(x) satisfies:
%e A155807 A(x) = 1 + x*A(x)^2 + x^2/2!*A(x)^6 + x^3/3!*A(x)^12 + x^4/4!*A(x)^20 +...
%e A155807 Let B(x) = A(x/B(x)) be the e.g.f. of A155806 then:
%e A155807 B(x) = 1 + x*B(x) + x^2/2!*B(x)^4 + x^3/3!*B(x)^9 + x^4/4!*B(x)^16 +...
%e A155807 B(x) = 1 + x + 3*x^2/2! + 22*x^3/3! + 269*x^4/4! + 4616*x^5/5! + 102847*x^6/6! +...
%o A155807 (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*(k+1))/k!+x*O(x^n))); n!*polcoeff(A,n)}
%Y A155807 Cf. A155804, A155805, A155806.
%K A155807 nonn
%O A155807 0,3
%A A155807 _Paul D. Hanna_, Jan 27 2009