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%I #2 Mar 30 2012 18:37:16
%S 1,1,4,53,2321,351010,189198136,371045084781,2686134761118382,
%T 72555484959298332681,7372783651816395650943931,
%U 2836907736669733620359204710274,4155363917021399525198623243750199333
%N L.g.f.: exp(Sum_{n>=1} a(n)*x^n/n) = 1 + x*exp(Sum_{n>=1} C(2n-1,n)*a(n)*x^n/n) where C(2n-1,n) = A001700(n-1).
%F L.g.f.: exp(Sum_{n>=1} a(n)*x^n/n) = 1 + x*G(x) where G(x) = g.f. of A158109.
%F exp(Sum_{n>=1} a(n)*x^n/n) = [1 + Sum_{n>=1} C(2n-1,n)*a(n)*x^n]/[1 + Sum_{n>=1} (C(2n-1,n)-1)*a(n)*x^n].
%e L.g.f.: A(x) = x + 1*x^2/2 + 4*x^3/3 + 53*x^4/4 + 2321*x^5/5 +...
%e exp(A(x)) = 1 + x + 2*x^2 + 15*x^3 + 479*x^4 + 58981*x^5 +...
%e exp(A(x)) = 1 + x*G(x) where G(x) is the g.f. of A158109 such that:
%e log(G(x)) = x + 3*1*x^2/2 + 10*4*x^3/3 + 35*53*x^4/4 + 126*2321*x^5/5 +...
%o (PARI) {a(n)=local(A=x+x^2);if(n==0,1,for(i=1,n-1,A=log(1+x*exp(sum(m=1,n,binomial(2*m-1,m)*x^m*polcoeff(A+x*O(x^m),m) )+x*O(x^n))));n*polcoeff(A,n))}
%Y Cf. A158109, A158258 (variant), A001700.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Mar 28 2009
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