Is a generalization of Vandermonde matrix with factorials invertible?

Question

Is this matrix invertible?

$A = \begin{bmatrix} 1 & a_1 & \frac{a_1^2}{2!} & \dots & \frac{a_1^m}{m!}\\ 1 & a_2 & \frac{a_2^2}{2!} & \dots & \frac{a_2^m}{m!}\\ \vdots &{ } & \vdots &{ } & \vdots\\ 1 & a_m & \frac{a_m^2}{2!} & \dots & \frac{a_m^m}{m!} \end{bmatrix}$

This matrix is closely related to the Vandermonde matrix but I don't know if/how I can use this fact to show that this matrix is invertible.

Answer 1

Based on the hint provided by @darij-grinberg:

If $$ is the Vandermonde matrix, we have

$\det()=1/(2!3!…!)\det()$

so the determinant of $A$ is non-zero.