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Metadata 
bibkey: hanna2025a380710
authors: Paul D. Hanna
year: 2025
title: 'OEIS A380710, g.f. satisfying A(x) = 1 + x*A(x)*abs(1/A(x)^2)'
doi: null
url: https://oeis.org/A380710
claim: 'G.f. A(x) satisfies A(x) = 1 + x*A(x)*abs( 1/A(x)^2 ). Conjecture: for n > 0, a(n) is odd iff n is a power of 2.'
strata_touched:
  - D5/S1/Recurrence/Invariants/AbsoluteReciprocalSquareParity
license: citation-only
triage: anchor

OEIS A380710

Paul D. Hanna’s entry of February 18, 2025 defines the generating function by the displayed equation and states the parity conjecture. Here abs takes the absolute value of each coefficient of the reciprocal-square series. The Lean module constructs the unique integer solution with constant coefficient one and proves the conjecture for every positive index.

Verified locator

  • URL: https://oeis.org/A380710