A177750 G.f. A(x) satisfies: A(A(A(x))) = A(A(x)) + x^2.

1, 1, -4, 32, -346, 4472, -65292, 1043753, -17921768, 326358300, -6247293860, 124904785856, -2595750453348, 55864370827852, -1241459233450784, 28421477429433280, -669049539675142690, 16169348706143246816

Offset

1,3

Links

Table of n, a(n) for n=1..18.

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

Cf. A141372 (unsigned inverse).

Sequence in context: A186391 A231446 A137432 * A304911 A224993 A357407

Adjacent sequences: A177747 A177748 A177749 * A177751 A177752 A177753

Keyword

sign

Author

Paul D. Hanna, May 12 2010

Status

approved