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PROG
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(PARI) {a(n)=local(A=x^2); for(i=1, n, A=intformal(2*serreverse(x - A*A' +O(x^(2*n))))); polcoeff(A, 2*n)}
for(n=1, 25, print1(a(n), ", "))
(PARI) {a(n)=local(A, G=x+x*O(x^n)); for(i=1, n, A=intformal(2*G); G = serreverse(x - 2*A*G +O(x^(2*n)))); polcoeff(A, 2*n)}
for(n=1, 25, print1(a(n), ", "))
(PARI) {Dx(n, F)=local(D=F); for(i=1, n, D=deriv(D)); D}
{a(n)=local(A=x^2); for(i=1, n, A = 2*intformal(x + sum(m=1, n+1, Dx(m-1, A^m*(A')^m/m!)) +O(x^(2*n+1)))); polcoeff(A, 2*n)}
for(n=1, 25, print1(a(n), ", "))
(PARI) {Dx(n, F)=local(D=F); for(i=1, n, D=deriv(D)); D}
{a(n)=local(A=x^2); for(i=1, n, A = 2*intformal(x*exp(sum(m=1, n, Dx(m-1, A^m*(A')^m/(m!*x))) +O(x^(2*n+1))))); polcoeff(A, 2*n)}
for(n=1, 25, print1(a(n), ", "))
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