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The number of derangements of n objects. more

The subfactorials up to 1015 :

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 10000 values, from 1 to 1.047⋅1035663).

n\r 0  1 
250005000 2 
3333333333334 3 
42500500025000 4 
520003000100010003000 5 
6166633333334166700 6 
71428214321450021422142 7 
812505000125001250012500 8 
933332222556055655505552223 9 
101000200010001000200010001000001000 10 

A pictorial representation of the table above
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.