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MATHEMATICA
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a[n_] := Module[{A = x}, Do[A = InverseSeries[x - D[A, x] A^2 + x O[x]^n, x], {n}]; SeriesCoefficient[A, {x, 0, n}]];
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PROG
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(PARI) {a(n) = local(A=x); for(i=1, n, A=serreverse(x - A^2*A' +x*O(x^n))); polcoeff(A, 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, B=x^2); for(i=1, n, A = x + sum(m=1, n, Dx(m-1, (A')^m*A^(2*m)/m!)) +O(x^(n+1))); polcoeff(A, 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, B=x^2); for(i=1, n, B=intformal(2*A); A = x*exp(sum(m=1, n, Dx(m-1, (A')^m*A^(2*m)/(m!*x))) +O(x^(n+1)))); polcoeff(A, n)}
for(n=1, 25, print1(a(n), ", "))
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