Dedicated to Archimedes on his 2300 th birthday Archimedes computed π very accurately. Much later, Ramanujan discovered several infinite series for 1/π that enables one to compute π even more accurately. The most impressive one is ([Ra]): ((a) k denotes, as usual, a(a + 1)...(a + k − 1).
We prove an explicit formula for the number of $n \times n$ upper triangular matrices, over $GF(q)$, whose square is the zero matrix. This formula was recently conjectured by Sasha Kirillov and Anna Melnikov.
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