Is there a formula that defines $$(1^1)(2^2)(3^3) . . . (n^n)?$$ Most of the texts on the internet tackle series with the same exponent, but how about this one?
Sorry for my mistakes
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11Is this what you seek for? http://mathworld.wolfram.com/Hyperfactorial.html – uranix May 22 '15 at 17:37
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@uranix thanks!!! – Airoh Borbe Jun 01 '15 at 14:43
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This question would be better if you explained the context in which the formula showed up, or at least what you were hoping to do with it. – goblin GONE Jul 03 '15 at 19:03
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The function you seek is called the hyperfactorial function, defined as $$H(n) = \prod_{k=1}^{n} k^k = 1^1 \cdot 2^2 \cdot 3^3 \cdots n^n$$
The OEIS sequence of integer values of $H(n)$ can be found here.
Zain Patel
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