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%I #4 Nov 18 2012 21:39:22
%S 1,1,2,8,46,334,2882,28604,320248,3993184,54942740,828086732,
%T 13586200504,241294019584,4615319816192,94629675177320,
%U 2070911506927360,48185049542009248,1187816429730925424,30923773410431125424,847808674826433774928,24414218135569507213312
%N G.f. satisfies: A(x) = Sum_{n>=0} n! * x^n * A(x)^(n*(n-1)/2).
%F G.f. satisfies: A(x) = B(x/A(x)) and A(x*B(x)) = B(x) where B(x) satisfies:
%F B(x) = Sum_{n>=0} n!*x^n * B(x)^(n*(n+1)/2) and is the g.f. of A219359.
%e G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 46*x^4 + 334*x^5 + 2882*x^6 +...
%e where
%e 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 (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 for(n=0, 25, print1(a(n), ", "))
%Y Cf. A155804, A219359.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Nov 18 2012
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