A049186 Revert transform of 2*x*(1-x-x^3-x^5+x^6)-x/(1+x).

1, 1, 3, 11, 45, 197, 901, 4259, 20643, 102035, 512365, 2606421, 13403715, 69568071, 363946211, 1917148173, 10160087333, 54132552109, 289790960735, 1557980372127, 8408281616305, 45536927325809, 247397689058521

Offset: 1

Author

Olivier Gérard

Keywords

• nonn

Comments

Sign diagram of generating sequence: +++-+-++--------...

2*x*(1-x-x^3-x^5+x^6)-x/(1+x) = x -x^2 -x^3 -x^4 -x^5 -x^6 +x^7 +x^8 -x^9 +x^10-+... = y <-> x= y +y^2 +3*y^3 +11*y^4 +45*y^5+... - R. J. Mathar, Jul 21 2023

Links

• Index entries for reversions of series

Crossrefs

Cf. A049189.

Programs

Maple

Order := 80:
g := 2*x*(1-x-x^3-x^5+x^6)-x/(1+x) ;
solve(series(g, x)=y, x) :
convert(%, polynom) :
seq(coeff(%, y, i), i=0..Order-1) ; # R. J. Mathar, Jul 24 2023

PARI

my(x='x+O('x^40)); Vec(serreverse(2*x*(1-x-x^3-x^5+x^6)-x/(1+x))) \\ Michel Marcus, Jul 21 2023

Extensions

NAME corrected by R. J. Mathar, Jul 21 2023