bibkey: chapoton2026a398690 authors: F. Chapoton year: 2026 title: “OEIS A398690, triangle of polynomials related to Verlinde numbers” doi: null url: https://oeis.org/A398690 claim: “Conjecture: The polynomials are palindromic.” strata_touched:

• D5/S3/Analytic/OeisA398690Palindromic license: citation-only triage: anchor

OEIS A398690

Chapoton’s entry defines the simplified Verlinde numbers by A(r,q) = (2q+1)^(-1) sum_{j=0}^{2q} (-1)^(rj) sin((2j+1)2pi/(8q+4))^(2-r) for r >= 3. For each n >= 0, it calls the numerator of sum_{q>=0} A(n+3,q) z^q, with denominator (1-z)^(n+1), the row polynomial. Its comment conjectures that these polynomials are palindromic. The separate A107735 array changes q to q/2 on even rows; that normalization is not used here.

The OEIS plain-text endpoint https://oeis.org/search?q=id:A398690&fmt=text was read on 2026-09-28 at revision 21 (Aug 08 2026 03:23:53). Its complete response has SHA-256 ed4ebe9572790d6a25cdb67b5779079efc85a47e6fe082050cba0debdabfbddf. The relevant comment lines still label palindromicity a conjecture and give the row-generating-function normalization above. A107735 cites Mukai (2003), p. 483 for the original array; whether that page contains a more general reciprocity theorem is not verified.

Verified locator

• Canonical entry URL: https://oeis.org/A398690
• Verified revision: 21, via the plain-text endpoint and response hash above.