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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
1
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Expression for summation involving factorial
It is known that $ \sum_{k = 0}^{n}
{n \choose k} = 2^n$ and $ \sum_{k = 0}^{n}
{n \choose k} (!k)= n!$. But is it known what
$ \sum_{k = 0}^{n } {n \choose k}(k!)$ is equal to?
-4
votes
1
answer
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Expression for a complex summation involving factorial [closed]
It is known that $\sum_{k = 0}^{n } {n \choose k}(k!) = \lfloor e \cdot n! \rfloor $ But is it known what $\sum_{p = 0}^{n} \sum_{q = 0}^{n - p} {n \choose p}{{n - p} \choose q} p! \cdot q! \cdot (n-p …