In trying to calculate the following sum:

[tex]

\sum_{i=1}^n{i^2}

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I found the following expansions:

[tex]

\sum_{i=1}^p \sum_{j=0}^{i-1} (-1)^j(i-j)^p {n+p-i+1\choose n-i} {p+1\choose j}

[/tex]

My question is: is there an easier or more intuitive way to compute the limit of the sum above?