what is the pattern

Question

what is the pattern 1,4,27,64

Answer 1

If the 4th term were 256, you would have 1¹, 2², 3³, 4⁴

As it stands, the pattern is not obvious.

Answer 2

WRONG attempt:

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1¹, 2², 3³, 4⁴, ...

which is x^x

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NEW Attempt:

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1² , 2² , 3³ , 4³ , ...

which is

x^{{[(x + 1) / 2] + 1}} for odd x,

and

x^{[(x / 2) + 1]} for even x