  Bilinear structure for the discrete Painlev\'e I equation is investigated.
The solution on semi-infinite lattice is given in terms of the Casorati
determinant of discrete Airy function. Based on this fact, the discrete
Painlev\'e I equation is naturally extended to a discrete coupled system.
Corresponding matrix model is also mentioned.

Exactly Solvable and Integrable Systems;High Energy Physics - Theory;Exactly Solvable and Integrable Systems