The conjectured strict recurrence inequality for Li coefficients

Let $\lambda_n$ denote the Li coefficients of the Riemann zeta function. In view of the recurrence relation for these coefficients, strict recurrence inequality for Li coefficients. For all integers $n\geq 3$, one has

$$\lambda_n>2\lambda_{n-1}-\lambda_{n-2}.$$

The paper presents this as a conjecture following a recurrence relation for Li coefficients. Under the Riemann hypothesis, a related bound is established for the absolute value of $\lambda_n+\lambda_{n-2}-2\lambda_{n-1}$, while the status of this strict inequality itself is not resolved in the supplied text.