  This paper is motivated by the need to improve the post-Newtonian (PN)
amplitude accuracy of waveforms for gravitational waves generated by
inspiralling compact binaries, both for use in data analysis and in the
comparison between post-Newtonian approximations and numerical relativity
computations. It presents: (i) the non-linear couplings between multipole
moments of general post-Newtonian matter sources up to order 3.5PN, including
all contributions from tails, tails-of-tails and the non-linear memory effect;
and (ii) the source mass-type octupole moment of (non-spinning) compact
binaries up to order 3PN, which permits to complete the expressions of the
octupole modes (3,3) and (3,1) of the gravitational waveform to order 3.5PN. At
this occasion we reconfirm by means of independent calculations our earlier
results concerning the source mass-type quadrupole moment to order 3PN. Related
discussions on factorized resummed waveforms and the occurence of logarithmic
contributions to high order are also included.
