Is there a formula to calculate $1^1 + 2^2 + 3^3 + ... + n^n$
I searched but didn't find a formula for increasing powers
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4I am not aware of any such formula, but you can find an asymptotic expansion as $n\to +\infty$. – Siméon Dec 21 '14 at 13:57
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If $a_n=\sum_{k=1}^n k^k$, then $a_{n+1}/a_n \rightarrow e\cdot n$. – Thomas Dec 21 '14 at 15:18