A Proof of Mathar's Recurrence Conjecture for OEIS A186185

Abstract

On May 7, 2024, R. J. Mathar contributed to OEIS A186185 a conjectured order-6 Precursive recurrence, with a matching asymptotic conjectured the same day by V. Kotesovec. We give a short proof, deriving an explicit cubic algebraic equation for the generating function from its defining functional equation and extracting the recurrence via the Bostan-Chyzak-Salvy algebraic-to-holonomic correspondence.