  In this paper, we introduce the notion of parabolic stable pairs on
Calabi-Yau 3-folds and invariants counting them. By applying the wall-crossing
formula developed by Joyce-Song, Kontsevich-Soibelman, we see that they are
related to generalized Donaldson-Thomas invariants counting one dimensional
semistable sheaves on Calabi-Yau 3-folds. Consequently, the conjectural
multiple cover formula of generalized DT invariants is shown to be equivalent
to a certain product expansion formula of the generating series of parabolic
stable pair invariants. The application of this result to the multiple cover
formula will be pursued in the subsequent paper.
