[R] how to construct a time series

[n.vialma at libero.it]

Hi,
I need to generate the time series of the production, but as I'm new to this 
topic I am not able to do that. This is what the time series should be:

PROD(t)=PROD(t,T)
PROD(t-1)=PROD(t-1,T)
PROD(t-2)=PROD(t-1)*PROD(t-2,T-1)/PROD(t-1,T-1)
PROD(t-3)=PROD(t-2)*PROD(t-3,T-2)/PROD(t-2,T-2)
...
...
...
from PROD(t-2)...it will get the same expression; where PROD(t,T) is the value 
of the production at t for the sample of firms presented at T and T-1;
Someone knows how to get it???
Thanks for your attention!!!