I am looking to see if there are any canonical references that deal with the following summation:
$$\sum_{i=1}^m{(m+1-i)i^p}$$
Here, $p\in \mathbb{N}$ I don't know if there has been published work with these. I have a particular generating function that I"m looking at
$$g(x)=\frac{1}{(1-x)^m(1-2x)^{m-1}...(1-(m-1)x)^2(1-mx)}$$
and i don't know if there are any papers or textbooks dealing with it. I do know it can be written as a double sum
$$\sum_{j=1}^m\sum_{i=1}^ji^p$$
And i know sums of powers can be expressed in terms of bernoulli numbers, but I can't crack the double sum and was wondering if it could be done using bernoulli numbers or some other type of combinatorical sequence of numbers.