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A320808 Regular tetrangle where T(n,k,i) is the number of nonnegative integer matrices up to row and column permutations with no zero rows or columns and k nonzero entries summing to n, with i columns.

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%I A320808 #10 Jul 09 2025 04:48:17
%S A320808 1,0,0,1,0,0,1,0,1,2,0,0,1,0,1,2,0,1,2,3,0,0,1,0,2,4,0,1,5,4,0,1,5,5,
%T A320808 5,0,0,1,0,2,4,0,2,10,8,0,1,9,13,7,0,1,5,12,9,7,0,0,1,0,3,6,0,3,16,12,
%U A320808 0,2,24,33,16,0,1,14,36,29,12,0,1,9,23,29
%N A320808 Regular tetrangle where T(n,k,i) is the number of nonnegative integer matrices up to row and column permutations with no zero rows or columns and k nonzero entries summing to n, with i columns.
%e A320808 Tetrangle begins:
%e A320808   1  0    0      0        0          0
%e A320808      0 1  0 1    0 1      0 1        0 1
%e A320808           0 1 2  0 1 2    0 2 4      0 2 4
%e A320808                  0 1 2 3  0 1 5 4    0 2 10 8
%e A320808                           0 1 5 5 5  0 1 9 13 7
%e A320808                                      0 1 5 12 9 7
%Y A320808 Triangle sums are A007716. Triangle of row sums is A320801. Triangle of column sums is A317533. Triangle of last columns (without its leading column 1,0,0,0,...) is A055884.
%Y A320808 Cf. A000219, A008284, A316980, A316983, A318805, A319616, A320796, A321194.
%K A320808 nonn,tabf
%O A320808 1,10
%A A320808 _Gus Wiseman_, Nov 09 2018