Determinant of a matrix with consecutive integers

by @ancient-tree · difficulty 29/100

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determinantmatrix
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Consider the matrices : A1=(1),A2=(1234),A3=(123456789),…A_1=(1), A_2=\left(\begin{array}{ll} 1 & 2 \\ 3 & 4 \end{array}\right), A_3=\left(\begin{array}{lll} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}\right), \ldots
What is the determinant of AnA_n ?

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