%I #17 Jan 28 2018 13:54:37
%S 1,2,2,1,3,1,3,1,1,3,2,1,4,2,1,4,2,1,1,5,2,1,1,5,3,1,1,5,3,2,1,5,3,2,
%T 1,1,6,3,2,1,1,6,3,2,1,1,1,6,4,2,1,1,1,6,4,2,2,1,1,6,4,3,2,1,1,7,4,3,
%U 2,1,1,7,4,3,2,1,1,1,7,5,3,2,1,1,1,8,5,3,2,1,1,1,8,5,3,2,2,1,1,8,5,3,2,2,1,1,1,9,5,3,2,2,1,1,1,8,5,4,3,2,1,1,1,9,5,4,3,2,1,1,1,9,6,4,3,2,1,1,1,9,6,4,3,2,1,1,1,1,9,6,4,3,2,2,1,1,1,10,6,4,3,2,2,1,1,1
%N Triangle read by rows in which row n gives a partition of n with the most subpartitions.
%C A partition and its conjugate have the same number of subpartitions; in the case of ties, we take the lexicographically earliest partition.
%H Mathoverflow, <a href="https://mathoverflow.net/questions/281313/upper-bound-for-number-of-subpartitions-of-a-partition/">Upper bound for number of subpartitions of a partition</a>, posted Sep 16 2017
%e Triangle begins
%e 1
%e 2
%e 2 1
%e 3 1
%e 3 1 1
%e 3 2 1
%e 4 2 1
%e 4 2 1 1
%e 5 2 1 1
%e 5 3 1 1
%e 5 3 2 1
%e 5 3 2 1 1
%e 6 3 2 1 1
%e 6 3 2 1 1 1
%e 6 4 2 1 1 1
%e 6 4 2 2 1 1
%e 6 4 3 2 1 1
%e 7 4 3 2 1 1
%e 7 4 3 2 1 1 1
%e 7 5 3 2 1 1 1
%e 8 5 3 2 1 1 1
%e 8 5 3 2 2 1 1
%e 8 5 3 2 2 1 1 1
%e 9 5 3 2 2 1 1 1
%e 8 5 4 3 2 1 1 1
%e 9 5 4 3 2 1 1 1
%e 9 6 4 3 2 1 1 1
%e 9 6 4 3 2 1 1 1 1
%e 9 6 4 3 2 2 1 1 1
%Y Cf. A116480, A117500.
%K nonn,tabf
%O 1,2
%A _Brian Hopkins_, Jan 04 2018