A137736 Number of set partitions of [n*(n-1)/2].

1, 1, 1, 5, 203, 115975, 1382958545, 474869816156751, 6160539404599934652455, 3819714729894818339975525681317, 139258505266263669602347053993654079693415, 359334085968622831041960188598043661065388726959079837

Offset

0,4

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).

See also A066655 which equals A066655(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).

Links

Table of n, a(n) for n=0..11.

Formula

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

a(n) = Sum_{k=0..(n^2-n)/2} Stirling2((n^2-n)/2,k).

Example

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

Maple

seq(combinat[bell](n*(n-1)/2), n=0..12);

Crossrefs

Cf. A000110, A006125, A066655, A135084, A135085, A161680.

Sequence in context: A208468 A070906 A208052 * A157389 A128678 A232987

Adjacent sequences: A137733 A137734 A137735 * A137737 A137738 A137739

Keyword

nonn

Author

Thomas Wieder, Feb 09 2008

Extensions

a(0)=1 prepended by Alois P. Heinz, Jul 24 2024

Status

approved