Is there a general product formula for $\sum\limits_{k=1}^{n} k^p$ [duplicate]

I'm familiar with Faulhaber's formula to express this sum as a much simpler one, but it appears that for any $p$ there's a product formula in $n$ for the sum e.g.:

$$\begin{align} & \sum\limits_{k=1}^{n} k^1=\frac{n(n+1)}{2} \\ & \sum\limits_{k=1}^{n} k^2=\frac{n(n+1)(2n+1)}{6} \\ & \sum\limits_{k=1}^{n} k^3=\frac{n^2(n+1)^2}{4} \end{align}$$

...and so forth. Is there a general product formula in $p$ and $n$ for this sum?

Solution 1:

This question was answered in a comment:

Yes: http://en.wikipedia.org/wiki/Faulhaber%27s_formula. – Martín-Blas Pérez Pinilla Feb 1 at 22:31