what is this sequence?

StatusX

Can anyone tell me if there is a closed form for the nth term in this sequence:

[tex]\sum_{k=0}^n \left( \begin{array} {cc} n \\ k \end{array} \right) a_k = \frac{1}{n}[/tex]

where a₀=0. This isn't homework, I'm just trying to find an expression for the nth integral of ln(x). So far I have:

[tex] \int_0^{x} dx_1 ... \int_0^{x_{n-1}} dx_n \mbox{ ln}(x) = \frac{x^n}{n!} (\mbox{ln}(x) + (-1)^n a_n )[/tex]

With a_n as defined above.