Constructing an entire function which has a zero of order $k^2$ for each $k \in \mathbb{Z} $

Question

I realize that such a function must exist because of the Weierstrass Factorization theorem, but how do I find the explicit form of it?

Answer 1

$\prod_{k=1}^{\infty}(1-\frac{z^4}{k^4})^{k^2}$ will do.
Note that this product converges based on the well known fact that
$\prod(1-|a_n|)$ and $\sum |a_n|$ converge(diverge) simultaneity.