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

1,3

Links

Table of n, a(n) for n=1..19.

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

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.

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 *)

Prog

(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))}

Crossrefs

Cf. A107700, A107701.

Sequence in context: A046245 A178248 A377599 * A079330 A059367 A309799

Adjacent sequences: A107696 A107697 A107698 * A107700 A107701 A107702

Keyword

sign

Author

Paul D. Hanna, May 21 2005

Status

approved