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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 vote
1 answer
364 views

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?
Arun Sen's user avatar
-4 votes
1 answer
106 views

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 …
Arun Sen's user avatar