1,3

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.

See also A135084 = A000110(2^n-1) and A135085 = A000110(2^n).

Thomas Wieder, Home Page.

Thomas Wieder, (Old) Home Page.

a(n) = Bell(n(n-1)/2) = A000110(n(n-1)/2)

a(4) = Bell(6) = 203.

for n from 1 to 10 do a(n):=bell((n^2-n)/2): print(a(n)); od:

Cf. A006125, A066655, A135084, A135085.

Sequence in context: A041775 A093976 A070906 this_sequence A157389 A128678 A012811

Adjacent sequences: A137733 A137734 A137735 this_sequence A137737 A137738 A137739

nonn

Thomas Wieder (thomas.wieder(AT)t-online.de), Feb 09 2008