bibkey: hanna2026a397902
authors: Paul D. Hanna
year: 2026
title: "OEIS A397902: square-exponent coefficient equations and dyadic parity support"
doi: null
url: https://oeis.org/A397902
claim: "Conjecture: for n > 2, a(n) is odd iff n is of the form 2^k, 2^k-1, 2^k-2, or 2^k-3 (k > 1)."
strata_touched:
  - D5/S1/Recurrence/SquareRows/SquareExponentDyadicSupport
license: citation-only
triage: anchor

OEIS A397902

The NAME reads: “G.f. A(x) satisfies [x^(n-1)] (1 - A(x))^(n^2) / (1 - n^2*x) = 0 for n > 1.” The FORMULA specifies A(x) = Sum_{n>=1} a(n)*x^n, fixing the zero constant coefficient and coefficient indexing. The formal domain is integer power series, and integer existence is part of the repository proof.

The comment quoted above is explicitly a conjecture in the retrieved entry. The entry credits Paul D. Hanna, July 20, 2026. The only HTML reference in the retrieved text is the table of 215 terms; the asymptotic formula credited to Vaclav Kotesovec does not concern parity. The b-file itself was not opened: ASSUMED-UNVERIFIED. No result is transferred from the cross-references A397591 or A397596, or from A397594/A397592.

The repository proof first normalizes each row by an exact derivative identity before reducing coefficients modulo two. It constructs the integer series and identifies its binary reduction using the Catalan equation. This proof is local work; it is not attributed to the OEIS entry.

Verified locator

url: https://oeis.org/A397902

Official text: https://oeis.org/search?q=id:A397902&fmt=text. The canonical URL above identifies the same entry. No DOI is assigned to this OEIS entry (doi: null).