Hello Eric, hello Gianluca,
Thanks a lot for your help - I realize I'm not really comfortable with Mathematica advanced syntax!
I was able to run your codes and to adapt yours Gianluca to my actual problem: manipulating Fourier series.
f[a_, b_, n_, x_] := Sum[a[i] Cos[i x] + b[i] Sin[i x], {i, 1, n}]
innerManipulate[n_Integer] :=
With[{cntrls =
Flatten[Table[{{{a[i], 0}, -1, 1}, {{b[i], 0}, -1, 1}}, {i, 1,
n}], 1]},
Manipulate @@ {Graphics[
Line@Table[{x, f[a, b, n, x]}, {x, -2 \[Pi],
2 \[Pi], .1}], Axes -> True], Sequence @@ cntrls}];
Manipulate[innerManipulate[n], {n, 1, 5, 1}]
Eric I don't know why I wasn't able to adapt your code, it looks like something gets wrong sometimes with initialization...
I'll now try to use Slider2D for Fourier coefficients so that it looks nicer - but I feel like it's going to be more than just a quick cosmetic change :D
Thank you again!