A177751 G.f. satisfies: A(A(A(A(x)))) = A(A(A(x))) + x^2.

1, 1, -6, 69, -1062, 19462, -402088, 9085441, -220353750, 5665524898, -153082742620, 4319464636306, -126674386447628, 3846946526572584, -120632792180721408, 3897081458373965713, -129457823080756611720

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: A214694 A347674 A234509 * A338176 A235327 A349556

Adjacent sequences: A177748 A177749 A177750 * A177752 A177753 A177754

Keyword

sign

Author

Paul D. Hanna, May 12 2010

Status

approved