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A331461 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.

%I A331461 #21 Feb 01 2020 22:37:53
%S A331461 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,
%T A331461 30,6,1,1,1,15,212,652,332,50,7,1,1,1,22,686,6369,6414,1062,80,8,1,1,
%U A331461 1,30,2389,79568,226041,56712,3117,120,9,1,1,1,42,8682,1256425,12848128,7295812,441881,8399,175,10,1,1
%N A331461 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.
%C A331461 A(n,k) is the number of non-isomorphic set multipartitions (multiset of sets) with k parts each part has size n.
%H A331461 Andrew Howroyd, <a href="/A331461/b331461.txt">Table of n, a(n) for n = 0..152</a>
%F A331461 A306018(n) = Sum_{d|n} A(n/d, d).
%e A331461 Array begins:
%e A331461 ===========================================================
%e A331461 n\k | 0 1 2   3    4       5          6              7
%e A331461 ----+-----------------------------------------------------
%e A331461   0 | 1 1 1   1    1       1          1              1 ...
%e A331461   1 | 1 1 2   3    5       7         11             15 ...
%e A331461   2 | 1 1 3   8   23      66        212            686 ...
%e A331461   3 | 1 1 4  16   93     652       6369          79568 ...
%e A331461   4 | 1 1 5  30  332    6414     226041       12848128 ...
%e A331461   5 | 1 1 6  50 1062   56712    7295812     1817321457 ...
%e A331461   6 | 1 1 7  80 3117  441881  195486906   200065951078 ...
%e A331461   7 | 1 1 8 120 8399 3006771 4298181107 17131523059493 ...
%e A331461   ...
%e A331461 The A(2,3) = 8 matrices are:
%e A331461   [1 0 0]  [1 1 0]  [1 1 1]  [1 1 0]  [1 1 0]  [1 1 1]  [1 1 0]  [1 1 1]
%e A331461   [1 0 0]  [1 0 0]  [1 0 0]  [1 1 0]  [1 0 1]  [1 1 0]  [1 0 1]  [1 1 1]
%e A331461   [0 1 0]  [0 1 0]  [0 1 0]  [0 0 1]  [0 1 0]  [0 0 1]  [0 1 1]
%e A331461   [0 1 0]  [0 0 1]  [0 0 1]  [0 0 1]  [0 0 1]
%e A331461   [0 0 1]  [0 0 1]
%e A331461   [0 0 1]
%o A331461 (PARI) \\ See A304942 for Blocks
%o A331461 T(n,k)={Blocks(k, n*k, n)}
%o A331461 { for(n=0, 7, for(k=0, 6, print1(T(n,k), ", ")); print) }
%Y A331461 Rows n=0..6 are A000012, A000041, A050535, A050913, A058783, A058784, A058785.
%Y A331461 Columns k=0..4 are A000012, A000012, A000027(n+1), A002624, A331720.
%Y A331461 Cf. A188392, A262809, A304942, A306018, A330942, A331485, A331508, A331509, A331510.
%K A331461 nonn,tabl
%O A331461 0,8
%A A331461 _Andrew Howroyd_, Jan 18 2020