TL;DR
This paper introduces Boolean-Narayana numbers, a refined class of combinatorial numbers, providing explicit formulas, recurrence relations, and properties like unimodality and log-concavity.
Contribution
It presents the first explicit formula and recurrence relation for Boolean-Narayana numbers, along with proofs of their unimodality, log-concavity, and real-rootedness.
Findings
Explicit formula for Boolean-Narayana numbers
Proved unimodality and log-concavity of their sequences
Established a three-term recurrence relation for their generating polynomials
Abstract
We introduce a refinement of Boolean-Catalan numbers and call them Boolean-Narayana numbers. We provide an explicit formula for these numbers, and prove unimodality, log-concavity, and real-roots-only results for their sequences. We also prove a three-term recurrence relation for their generating polynomials.
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