Is there a generalization of Faulhaber's formula is sense of summation bounds?

Question

Well known Faulhaber's formula is stated as

$$\sum _{k=1}^{n}k^{p}=\frac{1}{p+1}\sum _{j=0}^{p}{p+1 \choose j}B_{j}n^{p+1-j}$$

But is there any formula which holds for power sum of the form

$$\sum_{k=s}^{n}k^{p}, \quad s\in\mathbb{Z}?$$