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What is the least positive integer nnn that can be placed in the following expression:
n!(n+1)!(2n+1)!−1\large \color{#D61F06} n! (n+1)! (2n+1)! -1n!(n+1)!(2n+1)!−1
and yields a number ending with thirty digits of 9's.
Notation: ! is a factorial notation; for example, 8!=8×7×6×5×4×3×2×18! = 8\times7\times6\times5\times4\times 3\times2\times18!=8×7×6×5×4×3×2×1
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