%I #17 Jul 24 2024 09:47:16
%S 1,1,1,5,203,115975,1382958545,474869816156751,6160539404599934652455,
%T 3819714729894818339975525681317,
%U 139258505266263669602347053993654079693415,359334085968622831041960188598043661065388726959079837
%N Number of set partitions of [n*(n-1)/2].
%C 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.
%C The number of graphs on n labeled nodes is A006125(n)=sum(binomial((n^2-n)/2,k),k=0..(n^2-n)/2).
%C 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.
%C See also A135084 = A000110(2^n-1) and A135085 = A000110(2^n).
%F a(n) = Bell(n*(n-1)/2) = A000110(n*(n-1)/2).
%F a(n) = Sum_{k=0..(n^2-n)/2} Stirling2((n^2-n)/2,k).
%e a(4) = Bell(6) = 203.
%p seq(combinat[bell](n*(n-1)/2), n=0..12);
%Y Cf. A000110, A006125, A066655, A135084, A135085, A161680.
%K nonn
%O 0,4
%A _Thomas Wieder_, Feb 09 2008
%E a(0)=1 prepended by _Alois P. Heinz_, Jul 24 2024