Log-concavity of infinite product generating functions.

In the 1970s Nicolas proved that the coefficients p d (n) defined by the generating function ∑ n = 0 ∞ p d (n) q n = ∏ n = 1 ∞ 1 - q n - n d - 1 are log-concave for d = 1 . Recently, Ono, Pujahari, and Rolen have extended the result to d = 2 . Note that p 1 (n) = p (n) is the partition function and p 2 (n) = pp n is the number of plane partitions. In this paper, we invest in properties for p d (n) for general d. Let n ≥ 6 . Then p d (n) is almost log-concave for n divisible by 3 and almost strictly log-convex otherwise. [ABSTRACT FROM AUTHOR]