Numbers which count the ways in which n objects can be partitioned into non-empty subsets. more
The Bell numbers up to 10
15 :
1,
2,
5,
15,
52,
203,
877,
4140,
21147,
115975,
678570,
4213597,
27644437,
190899322,
1382958545,
10480142147,
82864869804,
682076806159,
5832742205057,
51724158235372,
474869816156751.
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 1.59⋅1027664).
n\r | 0 | 1 |
2 | 3333 | 6667 | 2 |
3 | 3076 | 4615 | 2309 | 3 |
4 | 1666 | 3334 | 1667 | 3333 | 4 |
5 | 1998 | 2047 | 1992 | 2172 | 1791 | 5 |
6 | 1026 | 3077 | 769 | 2050 | 1538 | 1540 | 6 |
7 | 1389 | 1405 | 1459 | 1405 | 1457 | 1472 | 1413 | 7 |
8 | 0 | 1666 | 1667 | 1667 | 1666 | 1668 | 0 | 1666 | 8 |
9 | 513 | 2563 | 513 | 256 | 1538 | 1796 | 2307 | 514 | 0 | 9 |
10 | 663 | 1364 | 656 | 1445 | 604 | 1335 | 683 | 1336 | 727 | 1187 | 10 |
11 | 883 | 992 | 892 | 887 | 923 | 919 | 908 | 878 | 903 | 891 | 924 |
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.