Heshan Aravinda

On Two Conjectures Related to the Boros-Moll Sequences

The Boros-Moll sequences $\{d_i(m)\}_{0\leq i\leq m}$ are defined as $$d_i(m)=2^{-2m}\sum_{k=i}^m 2^k \binom{2m-2k}{m-k}\binom{m+k}{k}\binom{k}{i}.$$ Consider the ratio sequence $$u_i(m)=\frac{d_{i-1}(m)d_{i+1}(m)}{d_i(m)^2}.$$ Chen and Gu conjectured that $\{u_i(m)\}_{2\leq i \leq m-2}$ is both reverse ultra log-conca...