Notation of a Cobb-Douglas function printed in 1989
Seems to be the second one, so $$ Q_t = A_t*(K_t^\alpha N^\beta_t T_t^\rho). $$

Two clues:


This is the usual specification.
On the top of page 14 it is written that
$$
w_t = \beta Q_t/N_t.
$$ 
Given a competitive labor market you have
$$
w_t = \frac{\partial Q_t}{\partial N_t}.
$$ 
If you assume the production function above then you indeed have
$$
\frac{\partial Q_t}{\partial N_t} = \beta Q_t/N_t.
$$