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%I #4 Mar 30 2012 18:37:26
%S 1,1,2,8,44,305,2521,24389,273990,3569531,53944055,944215131,
%T 19065096323,441174226355,11609627641798,344702951590401,
%U 11463058468995522,424180616752269732,17366249924363207650,782666399665891947949
%N G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^binomial(n+3,4).
%e G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 44*x^4 + 305*x^5 + 2521*x^6 +...
%e where the g.f. satisfies:
%e A(x) = 1 + x*A(x) + x^2*A(x)^5 + x^3*A(x)^15 + x^4*A(x)^35 + x^5*A(x)^70 + x^6*A(x)^126 + x^7*A(x)^210 +...+ x^n*A(x)^(n*(n+1)*(n+2)*(n+3)/4!) +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m*(A+x*O(x^n))^binomial(m+3,4)));polcoeff(A,n)}
%Y Cf. A107591, A191809, A191811, A191812.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 16 2011
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