|
|
A137736
|
|
Number of set partitions of n(n-1)/2.
|
|
1
|
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
Among n persons we have (n^2-n)/2 undirected relations. We can set partition these relations into (up to) A137736(n)=Bell((n^2-n)/2) sets.
The number of graphs on n labeled nodes is A006125(n)=sum(binomial((n^2-n)/2,k),k=0..(n^2-n)/2).
The number of set partitions of n(n-1)/2 is A137736(n)=sum(Stirling2((n^2-n)/2,k),k=0..(n^2-n)/2).
See also A066655 which equals A066555(n)=sum(P((n^2-n)/2,k),k=0..(n^2-n)/2) where P(n) is the number of integer partitions of n.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Bell(n(n-1)/2) = A000110(n(n-1)/2)
|
|
EXAMPLE
|
a(4) = Bell(6) = 203.
|
|
MAPLE
|
for n from 1 to 10 do a(n):=bell((n^2-n)/2): print(a(n)); od:
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|