Metadata
bibkey: sheppard2025a381423
authors: Mike Sheppard
year: 2025
title: "OEIS A381423, exponent of the maximal signed Hermite coefficient"
doi: null
url: https://oeis.org/A381423/internal
claim: "Differences are either 1 or -3"
strata_touched:
- D5/S3/Analytic/Polynomial/HermiteSignedMode
license: citation-only
triage: anchor
Verified locator
Source: https://oeis.org/A381423/internal, revision 8.
The unpaginated Comments conjecture begins: “Differences are either 1 or -3; more specifically the patterns (1,1,1,-3) or (1,1,1,1,-3), with position of those patterns appearing at linearly and quadratically spaced intervals, respectively. Seems to grow O(n^(1/2))”.
Only the independent first clause is addressed. The offset is zero. The source’s Mathematica code uses HermiteH and the first PositionLargest of CoefficientList; the PARI code scans exponents upward and returns the first coefficient equal to the signed maximum. At n=5 the example chooses exponent 1 in . Thus the target uses physicists normalization, signed order and the smallest exponent among ties. It does not assume the entry’s separate uniqueness assertion.
DLMF 18.5.13 gives the exact finite coefficient formula used for the polynomial. The research-stage bounded screen inspected OEIS, DLMF, the stated portions of Bonneux–Dunning–Stevens, arXiv:1909.03874v2, and Dudeja–Hsu Lemma 35. The latter’s normalized absolute coefficient bound does not settle a signed maximizer transition. No exact settlement was found in that inspected material; this is not a complete literature search or a claim of global priority.
The separate target is preregistered at #25634.