bibkey: werner2022a208509
authors: Knud Werner
year: 2022
title: "Conjectured coefficient formula in OEIS A208509"
doi: null
url: https://oeis.org/A208509
claim: "Conjecture: T(n,k) = binomial(n-1,2*k+1) + binomial(n,2*k+1). - _Knud Werner_, Jan 11 2022"
strata_touched:
  - D5/S1/Recurrence/Invariants/AffinePolynomialPairBinomialCoefficients
license: citation-only
triage: anchor

Werner’s coefficient conjecture

OEIS A208509 revision 28 records the conjecture attributed to Knud Werner in the FORMULA section. Clark Kimberling authored the sequence entry; this note attributes the conjecture, rather than the entry, to Werner. The jointly defined first family is A208508 revision 10.

The source laws are u(1,X)=v(1,X)=1, u(n,X)=u(n-1,X)+X*v(n-1,X), and v(n,X)=u(n-1,X)+v(n-1,X)+1 for n>=2. The formal statement uses polynomials over the integers, every n>=1, and every degree k>=0, extending rows by zero beyond their degree.

The bounded repository, pinned-Mathlib and third-party screen found no full supplier for this family. The bounded literature screen does not establish worldwide openness, originality or publication priority; unavailable searches, including a Semantic Scholar 429, are not zero hits.

Verified locator

• URL: https://oeis.org/A208509
• Original data: https://raw.githubusercontent.com/oeis/oeisdata/main/seq/A208/A208509.seq
• Companion: https://raw.githubusercontent.com/oeis/oeisdata/main/seq/A208/A208508.seq
• Locator: A208509 revision 28, FORMULA, Knud Werner, Jan 11 2022.

Conjecture: T(n,k) = binomial(n-1,2k+1) + binomial(n,2k+1). - Knud Werner, Jan 11 2022