This is related to this question : Can we conclude $n=p-1$?
For which positive integers $\ n\ $ is $$(2n)!+n!+1$$ a perfect power ?
For $\ n=1\ $ and $\ n = 2\ $ , we have a perfect power and there is no more perfect power for $\ n\le 8000\ $
Can we prove that $$(2n)!+n!+1$$ cannot be a perfect power for integer $\ n>2\ $ ?