This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A137736 #25 Jun 02 2025 15:17:22
%S A137736 1,1,1,5,203,115975,1382958545,474869816156751,6160539404599934652455,
%T A137736 3819714729894818339975525681317,
%U A137736 139258505266263669602347053993654079693415,359334085968622831041960188598043661065388726959079837
%N A137736 Number of set partitions of [n*(n-1)/2].
%C A137736 Among n persons we have (n^2-n)/2 undirected relations. We can set partition these relations into (up to) a(n) = Bell((n^2-n)/2) sets.
%C A137736 The number of graphs on n labeled nodes is A006125(n) = Sum_{k=0..(n^2-n)/2} binomial((n^2-n)/2,k).
%C A137736 See also A066655 which equals A066655(n) = Sum_{k=0..(n^2-n)/2} P((n^2-n)/2,k) where P(n) is the number of integer partitions of n.
%C A137736 See also A135084 = A000110(2^n-1) and A135085 = A000110(2^n).
%F A137736 a(n) = Bell(n*(n-1)/2) = A000110(n*(n-1)/2).
%F A137736 a(n) = Sum_{k=0..(n^2-n)/2} Stirling2((n^2-n)/2,k).
%e A137736 a(4) = Bell(6) = 203.
%p A137736 seq(combinat[bell](n*(n-1)/2), n=0..12);
%t A137736 a[n_]=BellB[n(n-1)/2];Array[a,12,0] (* _James C. McMahon_, Jun 02 2025 *)
%Y A137736 Cf. A000110, A006125, A066655, A135084, A135085, A161680.
%K A137736 nonn
%O A137736 0,4
%A A137736 _Thomas Wieder_, Feb 09 2008
%E A137736 a(0)=1 prepended by _Alois P. Heinz_, Jul 24 2024