Let and set of all permutations of the set for which Find the number of elements of the set
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Let $n \in \mathbb N$ and $A_n$ set of all permutations $(a_1, \ldots, a_n)$ of the set $\{1, 2, \ldots , n\}$ for which
$$k|2(a_1 + \cdots+ a_k), \text{ for all } 1 \leq k \leq n.$$
Find the number of elements of the set $A_n.$
Izvor: Međunarodna matematička olimpijada, shortlist 2008
Školjka 
and 
set of all permutations 
of the set 
for which
