Default Chebyshev U transform doubles the highest coefficient #272

On the default first-kind grid, chebyshevutransform doubles the highest U coefficient and ichebyshevutransform halves that mode.

We're sampling U₂(x) = 4x² - 1 on three points.

julia --startup-file=no --project -e '
using FastTransforms
@show chebyshevutransform([2.0, -1.0, 2.0])
@show ichebyshevutransform([0.0, 0.0, 1.0])
'

We get approximately [0, 0, 2.0] and [1, -0.5, 1] from the default paths.
The documented ordinary U expansion requires [0, 0, 1] and [2, -1, 2], respectively.

Versions — FastTransforms 0.17.3 at fc411c01a8422baf6c33356923111d7c2b9a8bed, Julia 1.10.12 and 1.11.9, FastTransforms_jll 0.6.4+0, FFTW 1.10.0, FFTW_jll 3.3.12+0, Linux x86_64.

The forward and inverse paths appear to omit the highest-mode normalization.

Happy to send a fix.

— ChipLab