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

%I #2 Mar 30 2012 18:37:10

%S 1,1,1,3,9,45,225,3015,22545,473625,4637025,191508075,2288273625,

%T 123786785925,1735168572225,276775700288175,4433024011291425,

%U 510439906229029425,9196849128341801025,3123191121957643317075

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

%e E.g.f.: A(x) = 1 + x + x^2/2! + 3*x^3/3! + 9*x^4/4! + 45*x^5/5! + 225*x^6/6! +...

%e Log(A(x)) = x + x^3/3 + x^5/5 + 3*x^7/7 + 9*x^9/9 + 45*x^11/11 + 225*x^13/13 +...

%o (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 Cf. A138314.

%K nonn

%O 0,4

%A _Paul D. Hanna_, Mar 13 2008