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A158266 G.f.: A(x) = exp( Sum_{n>=1} C(2n-1,n)^2*x^n/n ).

%I A158266 #6 Jun 04 2015 09:05:48
%S A158266 1,1,5,38,352,3659,41012,484739,5959417,75523708,980470867,
%T A158266 12980840984,174675568464,2382923659387,32890264803521,
%U A158266 458576476085929,6450351908991558,91437202854436755,1305115286958337403
%N A158266 G.f.: A(x) = exp( Sum_{n>=1} C(2n-1,n)^2*x^n/n ).
%C A158266 Compare g.f. to Catalan(x) = exp( Sum_{n>=1} C(2n-1,n)*x^n/n ), where C(2n-1,n) = A001700(n-1) and Catalan(x) is the g.f. of A000108(n) = C(2n,n)/(n+1).
%F A158266 a(n) = (1/n)*Sum_{k=1..n} C(2k-1,k)^2 * a(n-k) for n>0, with a(0)=1.
%F A158266 A(x) = exp( Sum_{n >= 1} 1/4*C(2*n,n)^2*x^n/n ). A(x)^4 is the o.g.f. for A224734. - _Peter Bala_, Jun 04 2015
%e A158266 G.f.: A(x) = 1 + x + 5*x^2 + 38*x^3 + 352*x^4 + 3659*x^5 + 41012*x^6 +...
%e A158266 log(A(x)) = x + 3^2*x^2/2 + 10^2*x^3/3 + 35^2*x^4/4 + 126^2*x^5/5 +...
%e A158266 log(C(x)) = x + 3*x^2/2 + 10*x^3/3 + 35*x^4/4 + 126*x^5/5 +...
%e A158266 C(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 42*x^5 +... (g.f. of A000108).
%o A158266 (PARI) {a(n)=polcoeff(exp(sum(m=1,n,binomial(2*m-1,m)^2*x^m/m)+x*O(x^n)),n)}
%o A158266 (PARI) {a(n)=if(n==0, 1, (1/n)*sum(k=1, n, binomial(2*k-1,k)^2*a(n-k)))}
%Y A158266 Cf. A001700, A000108, A224734.
%K A158266 nonn,easy
%O A158266 0,3
%A A158266 _Paul D. Hanna_, Apr 09 2009