Let Ωn stand for the volume of the unit ball in Rn for
n∈N. In the present paper, we prove that the sequence
Ωn1/(nlnn) is logarithmically convex and that the sequence
Ωn+11/[(n+1)ln(n+1)]Ωn1/(nlnn) is strictly
decreasing for n≥2. In addition, some monotonic and concave properties of
several functions relating to Ωn are extended and generalized.Comment: 12 page