TITLE: New formula for counting semi-standard Young tableaux?
QUESTION [7 upvotes]: I have a proof that given a partition $\lambda=(\lambda_1,\dots,\lambda_l)$
then the number of semi-standard Young tableaux (SSYT) of shape $\lambda$ with entries in $1,2,\dots, n$ is given by
$$\frac{1}{1!2!\cdots (n-1)!} \prod_{1\leq i\lt j\leq n} (\lambda_i-i)-(\lambda_j-j).$$
(We define $\lambda_j:=0$ if $j \gt l.$)
The product is also recognized as a Vandermonde determinant.
There are plenty of product formulas (over boxes in the tableau) 
and determinant formulas (but not in Vandermonde form, as far as I can tell) 
for the number of such SSYTs, but I have not seen a this particular one in the literature or in any article I've come across.
Is this formula known? Is this formula of any interest?

REPLY [4 votes]: I've finally found a place that gives this formula explicitly, without any need for piecing together or rewriting or taking limits using L'Hopital: Martin Aigner, A Course in Enumeration, Springer 2007, Section 8.5, formula (7) and the sentence that follows it.
I am wondering if anyone has ever given a bijective proof, though (after multiplying with the denominator).