The sequence A001711 satisfies a(n) - (2n+5)a(n-1) + (n+2)^2 a(n-2) = 0 for n >= 2, shown by substituting the closed form (1/4)(n+3)! (2 H_{n+3} - 3) and verifying that harmonic coefficients and constant terms both cancel to zero.
Niu,A short proof of Mathar’s 2014 recurrence conjecture for OEIS A002627
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A short proof of Mathar's 2020 recurrence conjecture for the generalized-Stirling sequence A001711
The sequence A001711 satisfies a(n) - (2n+5)a(n-1) + (n+2)^2 a(n-2) = 0 for n >= 2, shown by substituting the closed form (1/4)(n+3)! (2 H_{n+3} - 3) and verifying that harmonic coefficients and constant terms both cancel to zero.