(PARI) {a(n)=local(A=x+sum(k=3, n-1, a(k)*x^k)+x*O(x^n)); if(n==1, 1, if(n%2==0, 0, -polcoeff((subst(A, x, A-I*A^2)+I*subst(A, x, A-I*A^2+x*O(x^n))^2), n)/2))}
(PARI) /* Faster vectorized version: */
{ooo=100; A=[1]; B=x; C=(1-sqrt(1-4*(x+x^2+x*O(x^ooo))))/2;
A182399=[1];
A182399[n]=Vec((B+subst(C+x*O(x^n), x, serreverse(B)))/2)[n];
A=Vec(-I*subst(x*Ser(
A182399), x, I*serreverse(x+I*x^2+x^2*O(x^n))));
print1(A[n], ", "))}
(Maxima)
T(n, m):=if n=m then 1 else 1/2*(m/n*binomial(2*n-m-1, n-1)*(%i)^(n+m)*(-1)^n-(sum(T(k, m)*sum(T(n, i)*binomial(k, i-k)*(-%i)^(i-k), i, k, n), k, m+1, n-1)+sum(T(n, i)*binomial(m, i-m)*(-%i)^(i-m), i, m+1, n)));
