Demonstrates Turán inequalities for unimodal sequences, suggesting effective counting methods.
We derive an asymptotic expansion with effective error bound for $u(n)$, counting the number of unimodal sequences of size n. We prove that $u(n)$ satisfies the higher order Turán inequalities for n≥33 and that certain second j-shifted difference of $u(n)$ are positive.
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Banerjee et al. (2026) studied this question.
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