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%I #13 Sep 26 2013 03:59:38
%S 1,1,3,12,50,234,1125,5620,28753,150106,796240,4279232,23251672,
%T 127518750,704957715,3924307492,21978740682,123758612644,700204091361,
%U 3978636187708,22694470914700,129904466979030,745949776425002
%N G.f. satisfies: A(x) = F(x*A(x)), where F(x) is the g.f. of A094600.
%F a(n) = A094600(2*n)/(n+1) for n>=0.
%F G.f.: A(x) = exp( Sum_{n>=1} A094600(2*n-1)*x^n/n ).
%F G.f. satisfies: A(x) = A(y) + x*A(x)*A'(y)/A(y) + x^2*A(x)^2*A'(y) where y = x^2*A(x)^2.
%e G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 50*x^4 + 234*x^5 + 1125*x^6 + 5620*x^7 +...
%e where
%e A(x) = Sum_{n>=1} A094600(2*n)*x^n/(n+1), and
%e log(A(x)) = Sum_{n>=1} A094600(2*n-1)*x^n/n,
%e log(A(x)) = x + 5*x^2/2 + 28*x^3/3 + 145*x^4/4 + 831*x^5/5 + 4664*x^6/6 +...
%o (PARI) {a(n)=local(A=1+x); for(i=1,n, A=subst(A+x*A', x, x^2*A^2)+x*A*subst(A', x, x^2*A^2)/subst(A, x, x^2*A^2) +x*O(x^n)); polcoeff(A, n)}
%o for(n=0, 30, print1(a(n), ", "))
%Y Cf. A094600, A094558.
%K nonn
%O 0,3
%A _Paul D. Hanna_, May 13 2004
%E Entry revised by _Paul D. Hanna_, Apr 17 2013
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