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Contribution from _From _Paul D. Hanna_, Dec 06 2009: (Start)
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terms = 22; A[_] = 1; Do[A[x_] = 1 + x*A[x]*A[1 - 1/A[x]] + O[x]^j // Normal, {j, terms}]; CoefficientList[A[x], x] (* Jean-François Alcover, Jan 15 2018 *)
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A=(1+A*serreverse(x/(A+x*O(x^n))))^1); polcoeff(A, n)} \\ _Paul D. Hanna_, Dec 06 2009
for(n=0, 30, print1(a(n), ", ")) \\ _Paul D. Hanna_, Dec 06 2009
polcoeff(A+x*O(x^n), n)} \\ _Paul D. Hanna_, Dec 09 2013
for(n=0, 30, print1(a(n), ", ")) \\ _Paul D. Hanna_, Dec 09 2013
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Vaclav Kotesovec, <a href="/A088713/b088713.txt">Table of n, a(n) for n = 0..300</a>
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