real analysis - Evaluate $f(x)=sum_0^inftyfrac{x^n}{n!!}$.

A question from Introduction to Analysis by Arthur Mattuck:

Let $n!!=n(n-2)(n-4)\cdot…\cdot k$, where $k=1$ or $2$,depending on whether n is odd or even. (define $0!!=1$.)

Evaluate the sum $f(x)=\sum_0^\infty\frac{x^n}{n!!},$ using term-by-term differentiation and integration.

I think what the question asked is to give an explicit form for this sum.