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A331461
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Array read by antidiagonals: A(n,k) is the number of nonequivalent binary matrices with k columns and any number of nonzero rows with n ones in every column up to permutation of rows and columns.
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13
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1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 5, 8, 4, 1, 1, 1, 7, 23, 16, 5, 1, 1, 1, 11, 66, 93, 30, 6, 1, 1, 1, 15, 212, 652, 332, 50, 7, 1, 1, 1, 22, 686, 6369, 6414, 1062, 80, 8, 1, 1, 1, 30, 2389, 79568, 226041, 56712, 3117, 120, 9, 1, 1, 1, 42, 8682, 1256425, 12848128, 7295812, 441881, 8399, 175, 10, 1, 1
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OFFSET
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0,8
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COMMENTS
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A(n,k) is the number of non-isomorphic set multipartitions (multiset of sets) with k parts each part has size n.
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LINKS
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FORMULA
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EXAMPLE
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Array begins:
===========================================================
n\k | 0 1 2 3 4 5 6 7
----+-----------------------------------------------------
0 | 1 1 1 1 1 1 1 1 ...
1 | 1 1 2 3 5 7 11 15 ...
2 | 1 1 3 8 23 66 212 686 ...
3 | 1 1 4 16 93 652 6369 79568 ...
4 | 1 1 5 30 332 6414 226041 12848128 ...
5 | 1 1 6 50 1062 56712 7295812 1817321457 ...
6 | 1 1 7 80 3117 441881 195486906 200065951078 ...
7 | 1 1 8 120 8399 3006771 4298181107 17131523059493 ...
...
The A(2,3) = 8 matrices are:
[1 0 0] [1 1 0] [1 1 1] [1 1 0] [1 1 0] [1 1 1] [1 1 0] [1 1 1]
[1 0 0] [1 0 0] [1 0 0] [1 1 0] [1 0 1] [1 1 0] [1 0 1] [1 1 1]
[0 1 0] [0 1 0] [0 1 0] [0 0 1] [0 1 0] [0 0 1] [0 1 1]
[0 1 0] [0 0 1] [0 0 1] [0 0 1] [0 0 1]
[0 0 1] [0 0 1]
[0 0 1]
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PROG
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T(n, k)={Blocks(k, n*k, n)}
{ for(n=0, 7, for(k=0, 6, print1(T(n, k), ", ")); print) }
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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