bibkey: hanna2025a380066
authors: Paul D. Hanna
year: 2025
title: "OEIS A380066, bilateral product generating function"
doi: null
url: https://oeis.org/A380066
claim: "G.f. A(x) satisfies 1/2 = Sum_{n=-oo..+oo} x^n*A(x)^n * (A(x)^n + x)^(n-1) * (A(x) + x^n)^(n-1). Conjecture: for n > 0, a(n) == 2 (mod 4)."
strata_touched:
  - D5/S1/Recurrence/Bilateral/BilateralProductModFourUnitExponent
license: citation-only
triage: anchor

OEIS A380066

Paul D. Hanna’s entry, dated February 1, 2025, gives the bilateral product equation and the conjecture that every positive coefficient is two modulo four. The offset is zero and the constant coefficient is one. The formalization uses integer power series and reads the bilateral sum coefficientwise over symmetric windows.

The settlement proves existence and uniqueness of the normalized integral solution and proves the congruence for every positive index. The same contraction argument works uniformly for every exponent parameter at least one. The entry’s symmetry question under interchanging x and A is not addressed.

Verified locator

• URL: https://oeis.org/A380066