The number of minimally connected block designs
The formula \(a^{b-1} b^{a-1}\) is derived for the number of connected \(a\times b\) block designs having the least possible number, \(a+b-1\), of observations needed for connectedness. It is shown that this formula also arises as the number of labeled bicolored trees with a vertices of one color and b vertices of the other.
scientific article; zbMATH DE number 3974112