OFFSET
1,3
FORMULA
Unsigned series reversion yields A141372, the g.f. G(x) of which satisfies: G(x) = x + G(G(G(x)))^2.
EXAMPLE
G.f.: A(x) = x + x^2 - 4*x^3 + 32*x^4 - 346*x^5 + 4472*x^6 +...
Compare the iterations:
A(A(x)) = x +2*x^2 -6*x^3 +45*x^4 -472*x^5 +5990*x^6 -86368*x^7 +...
A(A(A(x))) = x +3*x^2 -6*x^3 +45*x^4 -472*x^5 +5990*x^6 -86368*x^7 +...
PROG
(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+B-subst(B, x, A), n)}
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, May 12 2010
STATUS
approved