convergence divergence - Is this convergent sum a constant?

I got this symbolic convergent sum from $\textit{Mathematica}$:
$$\sum _{k=1}^{\infty } \frac{k!}{(2 k)!}=\frac{1}{2} \sqrt[4]{e} \sqrt{\pi } \text{erf}\left(\frac{1}{2}\right)$$
Where $\text{erf}\left(\frac{1}{2}\right)$ can be found here.

Is this convergent sum a constant? I'm guessing "yes," but I have never encountered this kind of sum before.

Answer

Following the request by the OP, I'm posting this as an answer:

 The sum does not depend on anything, hence it is a number