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 A255404 #13 Sep 16 2019 19:54:48
%S A255404 1,1,2,1,1,1,1,1,1,1,4,3,2,1,4,2,1,2,1,2,2,1,1,1,2,1,1,1,3,1,1,1,1,2,
%T A255404 2,1,2,2,1,1,1,4,6,4,1,2,1,5,5,2,1,1,1,2,1,1,1,2,1,1,1,1,5,2,2,1,1,4,
%U A255404 1,1,2,3,1,8,2,1,1,3,1,1,1,3,1,1,3,1,6,1,1,1,1,1,1,1,1,1,1,1,5,1,3,2,1,1,1,1
%N A255404 Number of different integer partitions of n that produce the maximum number of set partitions for a set of cardinality n.
%C A255404 If n=Sum_i[n_i], the number of set partitions can be written as sp=n!/Prod_i,j(n_i!m_j!) where m_j is the multiplicity of the integer j in the n_i's. For certain integers, this number is maximized by more than one partition.
%H A255404 Alois P. Heinz, <a href="/A255404/b255404.txt">Table of n, a(n) for n = 0..1000</a>
%e A255404 For n=9, {1,1,2,2,3} maximizes the number of set partitions, while for n=10, this number is maximized by {1,2,3,4}, {1,1,2,3,3}, {1,2,2,2,3} and {1,1,1,2,2,3}.
%t A255404 Prod[l_] := Apply[Times, Map[#! &, l]]*
%t A255404 Apply[Times, Map[Count[l, #]! &, Range[Max[Length[l]]]]]
%t A255404 b[n_] := (Min[Map[Prod, IntegerPartitions[n]]])
%t A255404 a[n_] := Count[Map[Prod, IntegerPartitions[n]], b[n]]
%t A255404 Table[a[n], {n, 0, 20}] (* after A102356 *)
%Y A255404 Cf. A102356, A102456.
%K A255404 nonn
%O A255404 0,3
%A A255404 _Andrei Cretu_, Feb 22 2015
%E A255404 More terms from _Alois P. Heinz_, Feb 25 2015