Context
At the bottom of this page from Wolfram Mathworld on the Riemann zeta function, the following constants are defined in equations (133), (137), and (141), respectively:
\begin{align*} C_{1} &:= \sum_{n=2}^{\infty} \frac{\zeta(n)}{n!} \\ & \approx 1.078188729575818482758265436769832381707219, \\\qquad C_{2} &:= \sum_{n=1}^{\infty} \frac{\zeta(2n)}{n!} \\ & \approx 2.407446554790328514709486656223022725582266, \text{ and} \\ C_{3} &:= \sum_{n=1}^{\infty} \frac{\zeta(2n)}{(2n)!} \\ &\approx 0.869001991962908998811054805561395688892494.\end{align*} It is also stated that "These sums have no known closed-form expression".
However, it could be the case that there are conjectured closed forms for these constants that correspond to the actual values with a high degree of accuracy.
Question: Are there any of such conjectured closed forms for $C_{1}$, $C_{2}$, and $C_{3}$ ?
