%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