A107699 Bisection (odd-indexed terms) of A107700.

1, 1, -2, 13, -145, 2328, -49784, 1358965, -46076544, 1902202515, -94104681660, 5503867176832, -376096374571125, 29714871818774044, -2689473418781240320, 276562260699626541509, -32073434441440654231749, 4167256779254698145624064, -603002974281204853457239860

Offset: 1

Author

Paul D. Hanna, May 21 2005

Keywords

• sign

Links

• P. Majer, The functional equation f(f(x))=x+f(x)^2

Crossrefs

Cf. A107700, A107701.

Programs

Mathematica

a[n_] := Module[{A, B, F}, A = Series[x+x^2+x^(2*n), {x, 0, 2*n}]; If[n<1, 0, For[i=0, i <= 2*n, i++, F = x+2*A^2; B = InverseSeries[A]; A = (A+(B /. x -> F))/2]; SeriesCoefficient[A, {x, 0, 2*n-1}]]]; Table[a[n], {n, 1, 19}] (* Jean-François Alcover, Feb 04 2014, after PARI *)

PARI

{a(n)=local(A,B,F);A=x+x^2+x*O(x^(2*n));if(n<1,0, for(i=0,2*n,F=x+2*A^2;B=serreverse(A);A=(A+subst(B,x,F))/2); polcoeff(A,2*n-1,x))}

Formula

G.f.: A(x) = (G(x) - G(-x))/2, where G(x) is the g.f. of A107700 and satisfies: G(G(x)) = x + 2*G(x)^2.