  In this paper, we prove that the number of unimodal sequences of size $n$ is
log-concave. These are coefficients of a mixed false modular form and have a
Rademacher-type exact formula due to recent work of the second author and
Nazaroglu on false theta functions. Log-concavity and higher Tur\'{a}n
inequalities have been well-studied for (restricted) partitions and
coefficients of weakly holomorphic modular forms, and analytic proofs generally
require precise asymptotic series with error term. In this paper, we proceed
from the exact formula for unimodal sequences to carry out this calculation. We
expect our method applies to other exact formulas for coefficients of mixed
mock/false modular objects.
