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A155804 E.g.f. satisfies: A(x) = Sum_{n>=0} x^n/n! * A(x)^(n(n-1)/2).

%I A155804 #4 Nov 18 2012 21:34:54
%S A155804 1,1,1,4,19,161,1606,21022,323485,5874913,122077756,2871573596,
%T A155804 75437801539,2193468714373,70020045331510,2437979768144026,
%U A155804 92073099488632441,3753886179551636513,164556499026975482008
%N A155804 E.g.f. satisfies: A(x) = Sum_{n>=0} x^n/n! * A(x)^(n(n-1)/2).
%F A155804 E.g.f. satisfies: A(x) = B(x/A(x)) and A(x*B(x)) = B(x) where B(x) satisfies:
%F A155804 B(x) = Sum_{n>=0} x^n/n! * B(x)^(n*(n+1)/2) and is the e.g.f. of A155805.
%e A155804 E.g.f.: A(x) = 1 + x + x^2/2! + 4*x^3/3! + 19*x^4/4! + 161*x^5/5! +...
%e A155804 where e.g.f. A(x) satisfies:
%e A155804 A(x) = 1 + x + x^2/2!*A(x) + x^3/3!*A(x)^3 + x^4/4!*A(x)^6 + x^5/5!*A(x)^10 +...
%e A155804 Let B(x) = A(x*B(x)) be the e.g.f. of A155805 then:
%e A155804 B(x) = 1 + x*B(x) + x^2/2!*B(x)^3 + x^3/3!*B(x)^6 + x^4/4!*B(x)^10 +...
%e A155804 B(x) = 1 + x + 3*x^2/2! + 19*x^3/3! + 191*x^4/4! + 2656*x^5/5! + 47392*x^6/6! +...
%o A155804 (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)/2)/k!+x*O(x^n))); n!*polcoeff(A,n)}
%Y A155804 Cf. A155805, A155806, A155807, A107590, A219358.
%K A155804 nonn
%O A155804 0,4
%A A155804 _Paul D. Hanna_, Jan 27 2009