Sum of series: $1^1 + 2^2 + 3^3 + … + n^n$

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Searched every where on web but I couldn't find out the formula for this series.

That's why I am asking here.

I tried following following formula:

$((n*(n+1))/2)^n$

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The sequence of partial sums is on the OEIS, but no simple formula is listed there, which makes me think no such formula is known.