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A177751 G.f. satisfies: A(A(A(A(x)))) = A(A(A(x))) + x^2. 0
1, 1, -6, 69, -1062, 19462, -402088, 9085441, -220353750, 5665524898, -153082742620, 4319464636306, -126674386447628, 3846946526572584, -120632792180721408, 3897081458373965713, -129457823080756611720 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..17.

FORMULA

Unsigned series reversion yields A141383, the g.f. G(x) of which satisfies: G(x) = x + G(G(G(G(x))))^2.

EXAMPLE

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 +...

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+subst(B, x, A)-subst(B, x, B), n)}

CROSSREFS

Cf. A141383 (unsigned inverse).

Sequence in context: A258792 A214694 A234509 * A235327 A098639 A305110

Adjacent sequences:  A177748 A177749 A177750 * A177752 A177753 A177754

KEYWORD

sign

AUTHOR

Paul D. Hanna, May 12 2010

STATUS

approved

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Last modified April 6 18:51 EDT 2020. Contains 333286 sequences. (Running on oeis4.)