Does anybody know whether or not this sum has a closed form? $$f(x)=\sum_{n=0}^\infty \frac{x^n}{n!(2^n+1)}$$ I can't get WA to even understand it when I type it in.
For context, the reason I want to know is that I calculated it as the solution to the functional equation $$f(x)+f(2x)=e^x$$