So i am preparing for exam in cominatorics and reading a textbook, and this is the task can't solve:
Find formula for normalized 2 row latin rectangle number $L(n,2)$ The problem is I am really stuck at this problem. Where L(n,2) is the number of normalized 2 row latin rectangles.
Could help me to solve this task? I am really stuck at this problem
It is closely related to derangements
\begin{array}{c|lc} n & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline L(n,2) & 1 & 1 & 3 & 11 & 53 & 309 & 2119 \end{array}
$$ L(n,2) = \frac{!n}{n-1} $$
where a simple trick to calculate deragenements
$$!n = \lfloor \frac{n!}e + \frac12 \rfloor $$
see ref here