TITLE: number of nilpotent $n\times n$ matrices over $\mathbb F_2$
QUESTION [3 upvotes]: Is there an elegant way of the sequence 
$$c_n = \left|\{ M \in \mathbb F_2^{n\times n} : \exists k\in \mathbb N \text{ s.t. } M^k=0\}\right|$$
explicitly? (Number of nilpotent $n\times n $ matrices over $\mathbb F_2$.)

REPLY [2 votes]: It turns out that somebody has already solved this problem! You can even find your sequence at OEIS (A053763), where they write that
$$c_n = 2^{n^2-n}.$$
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