Text: Calculate the number of partitions p(n) of a finite set of n elements from n=1 to n=50. Or you can do it by hand without a computer or describe how to do it by hand.
Examples:
n=2, p(2)=2
{a,b}
{a},{b}
n=3, p(3)=5
{a,b,c}
{ab},{c}
{ac},{b}
{bc},{a}
{a},{b},{c}
n=4, p(4)=15
{abcd}, 1
{abc},{d}, 2
{acd},{b}, 3
{abd},{c}, 4
{bcd},{a}, 5
{ab},{cd}, 6
{ac},{bd}, 7
{ad},{bc}, 8
{ab},{c},{d}, 9
{ac},{b},{d}, 10
{ad},{b},{c}, 11
{bc},{a},{d}, 12
{cd},{a},{b}, 13
{bd},{a},{c}, 14
{a},{b},{c},{d}, 15