I am trying to use Faulhaber's formula to determine partial sums of a power series.
Faulhaber's formula is given by
$\sum_{k=1}^{n}{k^{p}} = \frac{1}{p+1}\sum_{i=1}^{p+1}{(-1)^{\delta_ip}{p+1\choose i}}B_{p+1-i}n^{i}$ where $\delta_ip$ is the Kronecker delta function and $B_{p+1-i}$ is the $p+1-i$th Bernoulli number.
My question is, what do I use for $i$ in the Kronecker delta function when using this formula?
For example, I am trying to derive the partial sum of the power series $\sum_{k=1}^{n}{k^2}$ but I don't see what I would use for $i$.