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Regular tetrangle where T(n,k,i) is the number of non-isomorphic multiset partitions of length i of multiset partitions of length k of multisets of size n.
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%I #5 Sep 05 2018 17:15:09

%S 1,2,2,2,3,4,4,3,4,3,5,14,14,9,20,9,5,14,9,5,7,28,28,33,80,33,16,68,

%T 52,16,7,28,33,16,7,11,69,69,104,266,104,74,356,282,74,29,199,253,118,

%U 29,11,69,104,74,29,11,15,134,134,294,800,294,263,1427,1164

%N Regular tetrangle where T(n,k,i) is the number of non-isomorphic multiset partitions of length i of multiset partitions of length k of multisets of size n.

%e Tetrangle begins:

%e 1 2 3 5 7

%e 2 2 4 4 14 14 28 28

%e 3 4 3 9 20 9 33 80 33

%e 5 14 9 5 16 68 52 16

%e 7 28 33 16 7

%e Non-isomorphic representatives of the T(4,3,2) = 20 multiset partitions:

%e {{{1}},{{1},{1,1}}} {{{1,1}},{{1},{1}}}

%e {{{1}},{{1},{1,2}}} {{{1,1}},{{1},{2}}}

%e {{{1}},{{1},{2,2}}} {{{1,1}},{{2},{2}}}

%e {{{1}},{{1},{2,3}}} {{{1,1}},{{2},{3}}}

%e {{{1}},{{2},{1,1}}} {{{1,2}},{{1},{1}}}

%e {{{1}},{{2},{1,2}}} {{{1,2}},{{1},{2}}}

%e {{{1}},{{2},{1,3}}} {{{1,2}},{{1},{3}}}

%e {{{1}},{{2},{3,4}}} {{{1,2}},{{3},{4}}}

%e {{{2}},{{1},{1,1}}} {{{2,3}},{{1},{1}}}

%e {{{2}},{{1},{1,3}}}

%e {{{2}},{{3},{1,1}}}

%Y Cf. A007716, A050336, A050338, A255906, A269134, A317533, A317791, A318393, A318399, A318564, A318565, A318566.

%K nonn,tabf

%O 1,2

%A _Gus Wiseman_, Sep 04 2018