skew young tableaux are simple combinatorial objects arising in the theory of symmetric functions and the representation theory of the symmetric group. the number $f^\sigma$ of (standard) skew young tableaux of skew shape $\sigma$ has a simple determinantal formula due to aitken. we will discuss some situations for which there exist other formulas or generating functions for $f^\sigma$. for instance, for certain skew shapes $\sigma$ the number $f^\sigma$ can be described in terms of euler numbers (the number of alternating permutations of $1,2,\dots,n$) using an analytic technique introduced by elkies and further developed by baryshnikov and romik. certain other sequences $\sigma_n$ of skew shapes have simple generating functions for the numbers $f^{\sigma_n}$, based on a well-known connection between determinants and generating functions.