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%I #14 Mar 29 2020 19:35:39
%S 1,1,3,7,21,54,167,491,1586,5132,17442,60399,216172,790436,2965333,
%T 11365813,44536775,178107679,726716229,3022464373,12807206008,
%U 55253891494,242585471236,1083255591604,4917631017573,22685090928596,106291554085987,505653658171936,2441383079595849
%N Number of nonnegative integer matrices with values summing to n, up to transposition and permutation of rows and columns.
%C Also the number of non-isomorphic pairs of set partitions of {1,...,n}.
%H Andrew Howroyd, <a href="/A318395/b318395.txt">Table of n, a(n) for n = 0..50</a>
%F a(n) = (A007716(n) + A316983(n))/2. - _Andrew Howroyd_, Sep 03 2018
%e Inequivalent representatives of the a(3) = 7 nonnegative integer matrices:
%e [3] [1 2] [1 1 1] [1 0] [0 1] [1 0 0] [1 0 0]
%e [0 2] [1 1] [0 1 1] [0 1 0]
%e [0 0 1]
%e Non-isomorphic representatives of the a(3) = 7 pairs of set partitions:
%e {{1,2,3}} {{1,2,3}}
%e {{1,2,3}} {{1},{2,3}}
%e {{1,2,3}} {{1},{2},{3}}
%e {{1},{2,3}} {{1},{2,3}}
%e {{1},{2,3}} {{2},{1,3}}
%e {{1},{2,3}} {{1},{2},{3}}
%e {{1},{2},{3}} {{1},{2},{3}}
%Y Cf. A000110, A000258, A001247, A007716, A008277, A049311, A059849, A060639, A116540, A181939, A316983, A318393.
%K nonn
%O 0,3
%A _Gus Wiseman_, Aug 25 2018
%E a(6)-a(25) from _Andrew Howroyd_, Sep 03 2018
%E Terms a(26) and beyond from _Andrew Howroyd_, Mar 29 2020
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