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 A320438 #16 Mar 06 2025 08:27:41
%S A320438 1,1,1,1,1,1,1,1,1,1,1,4,1,1,3,7,1,1,9,1,1,1,1,43,35,1,1,102,62,1,1,1,
%T A320438 1,68,595,1,1,17,187,871,1480,361,1,1,2650,657,1,1,9294,1,1,23728,1,1,
%U A320438 27763,4110,1,1,1850,25035,108516,157991,7636,1,1,11421,411474,1
%N A320438 Irregular triangle read by rows where T(n,k) is the number of set partitions of {1,...,n} with all block-sums equal to d, where d is the k-th divisor of n*(n+1)/2 that is >= n.
%e A320438 Triangle begins:
%e A320438 1
%e A320438 1
%e A320438 1 1
%e A320438 1 1
%e A320438 1 1
%e A320438 1 1
%e A320438 1 4 1
%e A320438 1 3 7 1
%e A320438 1 9 1
%e A320438 1 1
%e A320438 1 43 35 1
%e A320438 1 102 62 1
%e A320438 1 1
%e A320438 1 68 595 1
%e A320438 1 17 187 871 1480 361 1
%e A320438 1 2650 657 1
%e A320438 Row 8 counts the following set partitions:
%e A320438 {{18}{27}{36}{45}} {{1236}{48}{57}} {{12348}{567}} {{12345678}}
%e A320438 {{138}{246}{57}} {{12357}{468}}
%e A320438 {{156}{237}{48}} {{12456}{378}}
%e A320438 {{1278}{3456}}
%e A320438 {{1368}{2457}}
%e A320438 {{1458}{2367}}
%e A320438 {{1467}{2358}}
%t A320438 spsu[_,{}]:={{}};spsu[foo_,set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@spsu[Select[foo,Complement[#,Complement[set,s]]=={}&],Complement[set,s]]]/@Cases[foo,{i,___}];
%t A320438 Table[Length[spsu[Select[Subsets[Range[n]],Total[#]==d&],Range[n]]],{n,12},{d,Select[Divisors[n*(n+1)/2],#>=n&]}]
%Y A320438 Row lengths are A164978. Row sums are A035470.
%Y A320438 Cf. A000110, A000258, A008277, A112956, A164977, A275714, A279375, A300335, A320423, A320424, A321455, A321469.
%K A320438 nonn,tabf
%O A320438 1,12
%A A320438 _Gus Wiseman_, Jan 08 2019
%E A320438 More terms from _Jinyuan Wang_, Feb 27 2025
%E A320438 Name edited by _Peter Munn_, Mar 06 2025