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Is there any general formula to sum following series:

$$S = 1^1 + 2^2 + 3^3 + \dotsb+(n - 1)^{n - 1} + n^n, n \in N$$

I mean for $S = f(n)$, is there a formula to compute $f(n)$?
Regards, vishal.

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It seems to me a possible duplicate, but I don't remember exactly. –  vesszabo Jan 14 '13 at 19:01
    
Yes, indeed: look for Faulhaber's formula. –  Matemáticos Chibchas Jan 15 '13 at 5:40
1  
Nope, sorry. This is equivalent to the integral of $x^x$. Faulhaber's formula is about polynomials. –  Greg Ros Jan 15 '13 at 5:43
1  
In general, if there isn't an elementary integral for a function there will not be a partial sum formula either. –  Greg Ros Jan 15 '13 at 5:45
3  
I found the first few values (for $n = 1, \dots , 4$), and this sequence (not surprisingly) appears in OEIS. You can find more information there. –  JavaMan Jan 15 '13 at 5:52

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