What is (Fourier frame length/2 + 1)?
Using your notations: number_frequency_bin, i.e. the number of "non-redundant" frequency bins, the first (corresponding to the DC) and last (corresponding to Nyquist) ones being always real for a real signal. The first is a (normalized) sum of samples, the last a sum of samples with alternated signs (since  $e^{i\pi n }=(-1)^n$).