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Regular tetrangle where T(n,k,i) is the number of unlabeled connected multiset partitions of weight n with k vertices and i edges.
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%I #4 Nov 28 2018 08:02:57

%S 1,0,0,1,0,0,0,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,1,2,1,1,2,4,2,1,2,

%T 1,0,0,0,0,0,0,1,2,2,1,1,2,7,6,2,2,6,4,1,2,1,0,0,0,0,0,0,0,1,3,3,2,1,

%U 1,3,14,17,9,3,3,17,18,7,2,9,7,1,3,1,0,0

%N Regular tetrangle where T(n,k,i) is the number of unlabeled connected multiset partitions of weight n with k vertices and i edges.

%e Tetrangle begins:

%e 1

%e .

%e 0 0

%e 1

%e .

%e 0 0 0

%e 1 1

%e 1

%e .

%e 0 0 0 0

%e 1 1 1

%e 1 1

%e 1

%e .

%e 0 0 0 0 0

%e 1 2 1 1

%e 2 4 2

%e 1 2

%e 1

%e .

%e 0 0 0 0 0 0

%e 1 2 2 1 1

%e 2 7 6 2

%e 2 6 4

%e 1 2

%e 1

%e .

%e 0 0 0 0 0 0 0

%e 1 3 3 2 1 1

%e 3 14 17 9 3

%e 3 17 18 7

%e 2 9 7

%e 1 3

%e 1

%e .

%e 0 0 0 0 0 0 0 0

%e 1 3 4 3 2 1 1

%e 3 20 33 24 11 3

%e 4 33 59 35 10

%e 3 24 35 14

%e 2 11 10

%e 1 3

%e 1

%Y Triangle sums are A007718.

%Y Cf. A007716, A054923, A191646, A191970, A275421, A286520, A317533, A317672, A321155, A321254, A322114.

%K nonn,tabf

%O 0,27

%A _Gus Wiseman_, Nov 27 2018