New results on Identical Binomial Coefficient?

Question

Are there any nontrivial identical binomial coefficients found other than: $$ {16 \choose 2}={10 \choose 3}=120 \\ {21 \choose 2}={10 \choose 4}=210 \\ {56 \choose 2}={22 \choose 3}=1540 \\ {120 \choose 2}={36 \choose 3}=7140 \\ {153 \choose 2}={19 \choose 5}=11628 \\ {221 \choose 2}={17 \choose 8}=24310 \\ {78 \choose 2}={15 \choose 5}={14 \choose 6}=3003$$ and the infinite family (where $F_n$ is the $n$th fibonacci number): $$ {F_{2i+2}F_{2i+3} \choose F_{2i}F_{2i+3}}={F_{2i+2}F_{2i+3}-1 \choose F_{2i}F_{2i+3}+1}$$ By non-trivial I mean, of the shape ${n \choose k}$ where $2\leq k \leq \frac{1}{2}n $. This was conjectured to be the complete list in a paper from 1996: https://pdfs.semanticscholar.org/69fe/a6ef6f5ac5818538a86e98ddd9236a3310f7.pdf Are there any new results?