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A177751
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G.f. satisfies: A(A(A(A(x)))) = A(A(A(x))) + x^2.
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0
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1, 1, -6, 69, -1062, 19462, -402088, 9085441, -220353750, 5665524898, -153082742620, 4319464636306, -126674386447628, 3846946526572584, -120632792180721408, 3897081458373965713, -129457823080756611720
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OFFSET
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1,3
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LINKS
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FORMULA
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Unsigned series reversion yields A141383, the g.f. G(x) of which satisfies: G(x) = x + G(G(G(G(x))))^2.
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EXAMPLE
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G.f.: A(x) = x + x^2 - 6*x^3 + 69*x^4 - 1062*x^5 + 19462*x^6 +...
Compare the iterations:
A(A(A(x))) = x + 3*x^2 - 12*x^3 + 126*x^4 - 1856*x^5 + 33110*x^6 +...
A(A(A(A(x)))) = x + 4*x^2 - 12*x^3 + 126*x^4 - 1856*x^5 + 33110*x^6 +...
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PROG
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(PARI) {a(n)=local(A=x+sum(k=2, n-1, a(k)*x^k)+x*O(x^n), B=subst(A, x, A)); polcoeff(x+x^2+subst(B, x, A)-subst(B, x, B), n)}
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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