The growth series of the 2-extended affine Weyl group of type

The 2-extended affine Weyl groups are Weyl groups associated to the 2-extended affine root systems introduced by K. Saito [K. Saito, Extended affine root systems I, Publ. Res. Inst. Math. Sci. 21 (1985) 75–179]. We calculate the growth series of the 2-extended affine Weyl group of type with a generator system of a 2-toroidal sense.