Can someone help me with this one?

What is the norm of this functional on $l^2$? 

$$f(x) = \sum\_{n=1}^\infty \frac{3^n\cdot x\_n}{\sqrt{(n+1)!}}, \qquad x=(x\_1,x\_2,\ldots)\in l^2. $$

It is easy to see this functional is bounded ($\|f(x)\|\leq \sum\_{n=1}^\infty \frac{3^n}{\sqrt{(n+1)!}} \|x\_n\|$ and the series converges).

But I can't compute the exact norm. Any help appreciated.