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A219358 G.f. satisfies: A(x) = Sum_{n>=0} n! * x^n * A(x)^(n*(n-1)/2).

%I A219358 #8 Aug 28 2025 17:24:18
%S A219358 1,1,2,8,46,334,2882,28604,320248,3993184,54942740,828086732,
%T A219358 13586200504,241294019584,4615319816192,94629675177320,
%U A219358 2070911506927360,48185049542009248,1187816429730925424,30923773410431125424,847808674826433774928,24414218135569507213312
%N A219358 G.f. satisfies: A(x) = Sum_{n>=0} n! * x^n * A(x)^(n*(n-1)/2).
%F A219358 G.f. satisfies: A(x) = B(x/A(x)) and A(x*B(x)) = B(x) where B(x) satisfies:
%F A219358 B(x) = Sum_{n>=0} n!*x^n * B(x)^(n*(n+1)/2) and is the g.f. of A219359.
%e A219358 G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 46*x^4 + 334*x^5 + 2882*x^6 +...
%e A219358 where
%e A219358 A(x) = 1 + 1!*x + 2!*x^2*A(x) + 3!*x^3*A(x)^3 + 4!*x^4*A(x)^6 + 5!*x^5*A(x)^10 + 6!*x^6*A(x)^15 +...
%o A219358 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=sum(k=0,n,k!*x^k*(A+x*O(x^n))^(k*(k-1)/2)));polcoeff(A, n)}
%o A219358 for(n=0, 25, print1(a(n), ", "))
%Y A219358 Cf. A155804, A219359.
%K A219358 nonn,changed
%O A219358 0,3
%A A219358 _Paul D. Hanna_, Nov 18 2012