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A138314 E.g.f. satisfies: A(x) = exp( Sum_{n>=0} a(n)*x^(2n+1)/(2n+1)! ).

%I A138314 #10 Feb 26 2022 10:51:37
%S A138314 1,1,1,2,5,12,37,129,465,1912,8449,39481,200081,1069470,6043361,
%T A138314 36120082,226063729,1484564600,10184907985,72814137773,542009067393,
%U A138314 4188018707130,33562233856177,278441210021464,2387929437251657
%N A138314 E.g.f. satisfies: A(x) = exp( Sum_{n>=0} a(n)*x^(2n+1)/(2n+1)! ).
%F A138314 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-1,2*k) * a(k) * a(n-2*k-1). - _Ilya Gutkovskiy_, Feb 25 2022
%e A138314 E.g.f.: A(x) = 1 + x + x^2/2! + 2*x^3/3! + 5*x^4/4! + 12*x^5/5! + 37*x^6/6! +...
%e A138314 Log(A(x)) = x + x^3/3! + x^5/5! + 2*x^7/7! + 5*x^9/9! + 12*x^11/11! + 37*x^13/13! +...
%o A138314 (PARI) {a(n)=local(A=if(n==0,x,sum(k=0,n\2,a(k)*x^(2*k+1)/(2*k+1)!))); n!*polcoeff(exp(A+x*O(x^n)),n)}
%Y A138314 Cf. A138315.
%K A138314 nonn
%O A138314 0,4
%A A138314 _Paul D. Hanna_, Mar 13 2008