Lemma 2 in Knuth's "Notes on Open Addressing"
I think that the notes have been reported incorrectly. Indeed CruiskeenLawn, you are right. I've found some very old notes 
here which report the correct result. Indeed, in your copy, they simply forgot to add $\left[\begin{matrix} t\\ t\end{matrix}\right]$ term.
The Lemma you are looking for is on Page 2.