Substituting the closed form a(n) = (-1)^n (2 H_{n-3} - 3)(n-3)! into the left-hand side of the conjectured recurrence reduces it to the zero polynomial via harmonic number identities.
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A short proof of Mathar's 2021 recurrence conjecture for the Lehmer-Comtet diagonal A045406
Substituting the closed form a(n) = (-1)^n (2 H_{n-3} - 3)(n-3)! into the left-hand side of the conjectured recurrence reduces it to the zero polynomial via harmonic number identities.